Formal Neighborhood Research Articles

Twistor space for local systems on an open curve

Let [Formula: see text] be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank [Formula: see text]. We extend this construction to the case of any rank [Formula: see text], although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.

Decoding vibrant neighborhoods: Disparities between formal neighborhoods and urban villages in eye-level perceptions and physical environment

Vibrant neighborhoods play a pivotal role in the human well-being and social cohesion. However, existing research amalgamates vitality discussions of varied functions, failing to offer nuanced insights for specific neighborhood planning. Another gap emerges from the lack of research focusing on cultivating neighborhood vibrancy based on bottom-up spatial perceptions at the eye-level. Therefore, our study delves into the spatial and temporal disparities in vitality between formal neighborhoods and urban villages. Both real and virtual indicators are employed to measure the physical and digital vitality of neighborhoods. We incorporate eye-level perceptions as a new explanatory variable based on the physical environment. Our findings suggest that real vitality exhibits a modest morning and evening peak on weekends, while virtual vitality continually increases and peaks at night. In addition to enhancing green and enclosed neighborhood environments, improving public transportation options that replace reliance on motorized travel could facilitate formal neighborhood vitality. Regarding urban villages, clear rights-of-way can boost commuting efficiency, spatial accessibility and road safety, while the provision of ample public facilities and public spaces fosters the creation of “15-minute living circles.” The differentiated planning recommendations could offer valuable insights to promote livable neighborhoods and ultimately help to improve human well-being.

Modeling multi-scale influences on household lawncare decisions: Formal and informal neighborhood conforming effects on fertilizer use

Residential lawncare is understood to be a multi-scale process. In this article, we estimate a statistical model of household fertilizer decisions that characterizes household- and neighborhood-scale influences, emphasizing both informal and formal neighborhood effects. We develop a novel methodological approach that leverages spatially explicit parcel-level tax assessor data to examine informal neighborhood conforming pressures based on quantifiable metrics of property characteristics for each sampled household relative to surrounding neighbors. Using survey data from 2,635 households in the Baltimore metro region (in Maryland, USA), the statistical model is estimated for two sequenced decisions faced by households—whether to fertilize, and if so with what frequency. Results reveal that several household demographic and informal neighborhood variables are significant for one decision but not the other, demonstrating the importance of disaggregating these two decision stages. Informal neighborhood effects are primarily significant for the initial decision on whether to fertilize, perhaps because this decision is more readily observable by surrounding neighbors. Effects of formal neighborhood characteristics are significant in both fertilizer decisions but vary between homeowner and neighborhood associations and over the two sequential decisions. The widespread availability of parcel-level tax assessor data enables application of this novel approach in other regions to examine informal neighborhood pressures on fertilizer use or other lawncare behaviors.

Deformations of arcs and comparison of formal neighborhoods for a curve singularity

Abstract Let $ {\mathcal C} $ be an algebraic curve and c be an analytically irreducible singular point of ${\mathcal C}$ . The set ${\mathscr {L}_{\infty }}({\mathcal C})^c$ of arcs with origin c is an irreducible closed subset of the space of arcs on ${\mathcal C}$ . We obtain a presentation of the formal neighborhood of the generic point of this set which can be interpreted in terms of deformations of the generic arc defined by this point. This allows us to deduce a strong connection between the aforementioned formal neighborhood and the formal neighborhood in the arc space of any primitive parametrization of the singularity c. This may be interpreted as the fact that analytically along ${\mathscr {L}_{\infty }}({\mathcal C})^c$ the arc space is a product of a finite dimensional singularity and an infinite dimensional affine space.

Formal Neighbourhoods and Formal Models of Non-Degenerate Arcs

An important result about the geometry of the arc space of an algebraic variety is the theorem of Drinfeld–Grinberg–Kazhdan, representing the formal neighbourhood of a non-degenerate arc. We start with a brief review of some important results and notions. Then the complete proof of the theorem with examples is given. A generalization to the relative case is discussed for smooth and ´etale morphisms.

Creating a Dementia Friendly Community in an African American Neighborhood: Perspectives of People Living with Dementia, Care Partners, Stakeholders, and Community Residents.

A dementia friendly community allows people with dementia and their care partners to remain engaged in their community well into the disease. This study presents the results of primary research aimed at exploring perceptions regarding building a dementia friendly community in an African American neighborhood in northeast Florida. Twelve focus groups and five interviews were conducted with people living with dementia, informal and formal care partners, community stakeholders and neighborhood residents, and analyzed using a grounded theory approach. Three main themes emerged from the analyses, including (1) perceived needs, (2) facilitators and barriers to being dementia friendly, and (3) opportunities for the community to become more dementia friendly. Study findings highlight the unique needs of a single African American neighborhood and the importance of culturally tailoring the dementia friendly model to diverse communities.

A Study on Transformation of Housing Typology and Its Environmental and Social Effects on the Living Conditions of Residents in Planned Residential Neighborhoods of Kabul City

This study examines the transformation in housing typology from low-rise to apartment buildings in the formal neighborhood of Kabul city. These formal neighborhoods were developed according to plans from 1978. The majority of these neighborhoods were designed with detached houses that had courtyards. Literature reviews, field visits, opinions of residents, and a planning organization provided data for this study. In this study, the transformation of housing in planned neighborhoods is analyzed in relation to their social and environmental impacts. Researchers determined how varying housing typologies affected residents’ health and quality of life in these planned neighborhoods. Initially, we assessed the physical characteristics of the study area and evaluated how much transformation volume is present in the study area. Second, we examined residents’ views of residential development and its impacts, as well as their daily lives. In order to identify the relationship between these two aspects, the study examined the characteristics of the area (variables) from the perspectives of privacy, natural light, shading, sound pollution, air pollution, and energy use. We used several criteria to evaluate the accuracy of the physical characteristics and the respondents’ opinions. Lastly, we provided some recommendations and solutions to improve the current situation.

Neighbourhood participation and social inclusion: Case studies of Calgary, Alberta

Existing neighbourhood research suggests growing socio-spatial inequalities and decreased participation and social cohesion in cities across North America. This paper uses a multiple case study design and qualitative, in-depth interviews to explore individuals’ experiences of participation in diverse neighbourhoods in Calgary, Alberta, Canada. Based on thematic analysis of interviews, it identifies four types of formal neighbourhood participation (stepping up, speaking out, addressing needs, and showing up) and six types of informal participation in which residents engaged (networking, caring, reciprocating, working together, watching out, and getting out). These empirical findings offer rich qualitative perspectives on neighbourhood social capital, also drawing attention to the intersectional factors and complex power dynamics that influence how residents participate in neighbourhoods and neighbouring behaviours. Overall, the paper highlights the potential for community-based organizations to foster more inclusive participation, while also shaping how place-based inequalities play out.

The local information of difference equations

We give a definition for the restriction of a difference module on the affine line to a formal neighborhood of an orbit, trying to mimic the analogous definition and properties for a D-module. We show that this definition is reasonable in two ways. First, we show that specifying a difference module on the affine line is equivalent to giving its restriction to the complement of an orbit, together with its restriction to a neighborhood of an orbit and an isomorphism between the restriction of both to the intersection. We also give a definition for vanishing cycles of a difference module and define a local Mellin transform, which is an equivalence between vanishing cycles of a difference module and nearby cycles of its Mellin transform, a D-module.

Convergence of the mirror to a rational elliptic surface

The construction introduced by Gross, Hacking and Keel allows one to construct a formal mirror family to a pair $(S,D)$ where $S$ is a smooth rational projective surface and $D$ a certain type of Weil divisor supporting an ample or anti-ample class. In that paper they proved two convergence results. Firstly that if the intersection matrix of $D$ is not negative semi-definite then the family they construct lifts to an algebraic family. Secondly they prove that if the intersection matrix is negative definite then their construction lifts along certain analytic strata on the base, and then over a formal neighbourhood of this. In the original version of that paper they claimed that if the intersection matrix were negative semi-definite then family in fact extends over an analytic neighbourhood of the origin but gave an incorrect proof. In this paper we correct this error. We explain how the general Gross-Siebert program can be used to reduce construction of the mirror to such a surface to calculating certain relative Gromov-Witten invariants. We then relate these invariants to the invariants of a new space where we can find explicit formulae for the invariants. From this we deduce analytic convergence of the mirror family, at least when the original surface has an $I_4$ fibre.

Informalising formality: the construction of penghuqu in an urban redevelopment project in China

When applying informality in China, researchers always focus on urbanised villages with informal property ownership. Albeit important, property ownership is merely one parameter of informality. Inspired by the postcolonial urban theory, recent debates conceptualise informality in a relational way. This article adopts this dynamic informal-formal framework to explore the redevelopment of penghuqu in China. Penghuqu can be conceived as informality due to its physical conditions, but it is also an ambiguous category that leaves the local state with the space of discretion. By looking at the largest penghuqu redevelopment project in Sichuan, this article demonstrates that under the shield of penghuqu, the local government can deconstruct formal neighbourhood and informalise it as penghuqu, to meet with different political demands. By doing so, this article attempts to empirically add more variants to informal settlements, and theoretically further extend the ongoing debate that conceptualises informality in a relational way.

Serre–Tate theory for Shimura varieties of Hodge type

We study the formal neighbourhood of a point in the \(\mu \)-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a “shifted cascade”. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization in terms of its endomorphisms, analogous to the Serre–Tate canonical lift of an ordinary abelian variety.

Stacky GKM graphs and orbifold Gromov–Witten theory

A smooth GKM stack is a smooth Deligne-Mumford stack equipped with an action of an algebraic torus $T$, with only finitely many zero-dimensional and one-dimensional orbits.(i) We define the stacky GKM graph of a smooth GKM stack, under the mild assumption that any one-dimensional $T$-orbit closure contains at least one $T$ fixed point. The stacky GKM graph is a decorated graph which contains enough information to reconstruct the $T$-equivariant formal neighborhood of the $1$-skeleton (union of zero-dimensional and one-dimensional $T$-orbits) as a formal smooth DM stack equipped with a $T$-action.(ii) We axiomize the definition of a stacky GKM graph and introduce abstract stacky GKM graphs which are more general than stacky GKM graphs of honest smooth GKM stacks. From an abstract GKM graph we construct a formal smooth GKM stack.(iii) We define equivariant orbifold Gromov–Witten invariants of smooth GKM stacks, as well as formal equivariant orbifold Gromov–Witten invariants of formal smooth GKM stacks. These invariants can be computed by virtual localization and depend only the stacky GKM graph or the abstract stacky GKM graph. Formal equivariant orbifold Gromov–Witten invariants of the stacky GKM graph of a smooth GKM stack $\mathcal{X}$ are refinements of equivariant orbifold Gromov–Witten invariants of $\mathcal{X}$.

Derived geometry of the first formal neighbourhood of a smooth analytic cycle

If X is a smooth scheme of characteristic zero or a complex analytic manifold, and S is a locally split infinitesimal thickening of X, we compute explicitly the derived self-intersection of X in S.

RESIDENTIAL RELOCATION AND CHILDREN’S SATISFACTION WITH MASS HOUSING

This article investigates the effects of relocation on children’s satisfaction with mass housing built in the context of squatter housing regeneration. The results are based on a survey and group interviews with 137 nine-to-twelve-year-old children living in three mass housing developments in Ankara, Turkey. At the home level, it was found that while there was no significant change in the satisfaction level of children who moved to an outer-city mass housing development, satisfaction scores significantly increased among children who moved to inner-city estates. Moving from squatter or non-squatter housing did not significantly influence children’s dwelling satisfaction. At the neighbourhood level, regardless of their location in the city, satisfaction scores significantly decreased among children who moved from a formal neighbourhood; no significant change was observed among children who moved from a squatter settlement. Depending on where they moved from and their current place of residence, children explained the change in their residential satisfaction by referring to different dwelling and neighbourhood characteristics. Nevertheless, after relocation, all children mentioned some issues, such as the loss of home gardens, low-traffic volume streets, traditional commercial establishments, and parks and playgrounds with diverse activity areas and furniture.

The Structure of the Grothendieck Rings of Wreath Product Deligne Categories and their Generalisations

Abstract Given a tensor category $\mathcal{C}$ over an algebraically closed field of characteristic zero, we may form the wreath product category $\mathcal{W}_n(\mathcal{C})$. It was shown in [10] that the Grothendieck rings of these wreath product categories stabilise in some sense as $n \to \infty $. The resulting “limit” ring, $\mathcal{G}_\infty ^{\mathbb{Z}}(\mathcal{C})$, is isomorphic to the Grothendieck ring of the wreath product Deligne category $S_t(\mathcal{C})$ as defined by [9] (although it is also related to $FI_G$-modules). This ring only depends on the Grothendieck ring $\mathcal{G}(\mathcal{C})$. Given a ring $R$ that is free as a $\mathbb{Z}$-module, we construct a ring $\mathcal{G}_\infty ^{\mathbb{Z}}(R)$ that specialises to $\mathcal{G}_\infty ^{\mathbb{Z}}(\mathcal{C})$ when $R = \mathcal{G}(\mathcal{C})$. We give a description of $\mathcal{G}_\infty ^{\mathbb{Z}}(R)$ using generators very similar to the basic hooks of [5]. We also show that $\mathcal{G}_\infty ^{\mathbb{Z}}(R)$ is a $\lambda $-ring wherever $R$ is and that $\mathcal{G}_\infty ^{\mathbb{Z}}(R)$ is (unconditionally) a Hopf algebra. Finally, we show that $\mathcal{G}_\infty ^{\mathbb{Z}}(R)$ is isomorphic to the Hopf algebra of distributions on the formal neighbourhood of the identity in $(W\otimes _{\mathbb{Z}} R)^\times $, where $W$ is the ring of Big Witt Vectors.

Finite formal model of toric singularities

We study the formal neighborhoods at rational non-degenerate arcs of the arc scheme associated with a toric variety. The first main result of this article shows that these formal neighborhoods are generically constant on each Nash component of the variety. Furthermore, using our previous work, we attach to every such formal neighborhood, and in fact to every toric valuation, a minimal formal model (in the class of stable isomorphisms) which can be interpreted as a measure of the singularities of the base-variety. As a second main statement, for a large class of toric valuations, we compute the dimension and the embedding dimension of such minimal formal models, and we relate the latter to the Mather discrepancy. The class includes the strongly essential valuations, that is to say those the center of which is a divisor in the exceptional locus of every resolution of singularities of the variety. We also obtain a similar result for monomial curves.

An application of Cartan's equivalence method to Hirschowitz's conjecture on the formal principle

A conjecture of Hirschowitz's predicts that a globally generated vector bundle $W$ on a compact complex manifold $A$ satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in the underlying complex manifold of the vector bundle $W$. By applying Cartan's equivalence method to a suitable differential system on the universal family of the Douady space of the complex manifold, we prove that this conjecture is true if $A$ is a Fano manifold, or if the global sections of $W$ separate points of $A$. Our method shows more generally that for any unobstructed compact submanifold $A$ in a complex manifold, if the normal bundle is globally generated and its sections separate points of $A$, then a sufficiently general deformation of $A$ satisfies the formal principle. In particular, a sufficiently general smooth free rational curve on a complex manifold satisfies the formal principle.

The Ext algebra of a quantized cycle

Given a quantized analytic cycle $(X, \sigma)$ in $Y$, we give a categorical Lie-theoretic interpretation of a geometric condition, discovered by Shilin Yu, that involves the second formal neighbourhood of $X$ in $Y$. If this condition (that we call tameness) is satisfied, we prove that the derived Ext algebra $\mathcal{RH}om_{\mathcal{O}_Y}(\mathcal{O}_X, \mathcal{O}_X)$ is isomorphic to the universal enveloping algebra of the shifted normal bundle $\mathrm{N}_{X/Y}[-1]$ endowed with a specific Lie structure, strengthening an earlier result of C\u{a}ld\u{a}raru, Tu, and the first author This approach allows to get some conceptual proofs of many important results in the theory: in the case of the diagonal embedding, we recover former results of Kapranov, Markarian, and Ramadoss about (a) the Lie structure on the shifted tangent bundle $\mathrm{T}_X[-1]$ (b) the corresponding universal enveloping algebra (c) the calculation of Kapranov's big Chern classes. We also give a new Lie-theoretic proof of Yu's result for the explicit calculation of the quantized cycle class in the tame case: it is the Duflo element of the Lie algebra object $\mathrm{N}_{X/Y}[-1]$.

On central leaves of Hodge-type Shimura varieties with parahoric level structure

Kisin and Pappas (Publ Math Inst Hautes Études Sci, 2018) constructed integral models of Hodge-type Shimura varieties with parahoric level structure at $$p>2$$ , such that the formal neighbourhood of a mod p point can be interpreted as a deformation space of p-divisible group with some Tate cycles (generalising Faltings’ construction). In this paper, we study the central leaf and the closed Newton stratum in the formal neighbourhoods of mod p points of Kisin–Pappas integral models with parahoric level structure; namely, we obtain the dimension of central leaves and the almost product structure of Newton strata. In the case of hyperspecial level structure (i.e., in the good reduction case), our main results were already obtained by Hamacher (Math Z 287(3–4):1255–1277, 2017), and we show that the result of this paper holds for ramified groups as well.