Blow-up Of Projective Space Research Articles

Seshadri constants on some blow-ups of projective spaces

Let [Formula: see text] denote the blow-up of [Formula: see text] along [Formula: see text] general lines and [Formula: see text] general points. In this paper, we focus on [Formula: see text]-very ample line bundles on [Formula: see text] and investigate their Seshadri constants with some restrictions on [Formula: see text]. Additionally, we compute the nef cone of [Formula: see text] for [Formula: see text] and study the Seshadri constants of some ample line bundles on it. We also examine the Seshadri constants of some ample line bundles on [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text].

The Verlinde traces for SU_{X}(2,xi ) and blow-ups

Given a compact Riemann surface X of genus at least 2 with automorphism group G, we provide formulae that enable us to compute traces of automorphisms of X on the space of global sections of G-linearized line bundles defined on certain blow-ups of projective spaces along the curve X. The method is an adaptation of one used by Thaddeus to compute the dimensions of those spaces. In particular, we can compute the traces of automorphisms of X on the Verlinde spaces corresponding to the moduli space SU_{X}(2,xi ) when xi is a line bundle G-linearized of suitable degree.

Projective bundles and blow-ups of projective spaces

The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.

A Leray Model for the Orlik–Solomon Algebra

Abstract We construct a combinatorial generalization of the Leray models for hyperplane arrangement complements. Given a matroid and some combinatorial blow-up data, we give a presentation for a bigraded (commutative) differential graded algebra. If the matroid is realizable over $\mathbb {C}$, this is the familiar Morgan model for a hyperplane arrangement complement, embedded in a blowup of projective space. In general, we obtain a cdga that interpolates between the Chow ring of a matroid and the Orlik–Solomon algebra. Our construction can also be expressed in terms of sheaves on combinatorial blowups of geometric lattices. As a key technical device, we construct a monomial basis via a Gröbner basis for the ideal of relations. Combining these ingredients, we show that our algebra is quasi-isomorphic to the classical Orlik–Solomon algebra of the matroid.

EFFECTIVE CYCLES ON SOME LINEAR BLOWUPS OF PROJECTIVE SPACES

We compute cones of effective cycles on some blowups of projective spaces in general sets of lines.

Divisors on matroids and their volumes

The classical volume polynomial in algebraic geometry measures the degrees of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial for matroids, and give a complete combinatorial formula. For a realizable matroid, we thus obtain an explicit formula for the classical volume polynomial of the associated wonderful compactification. We then introduce a new invariant called the shifted rank volume of a matroid as a particular specialization of its volume polynomial, and discuss its algebro-geometric and combinatorial properties in connection to linear series on blow-ups of projective spaces.

Explicit log Fano structures on blow-ups of projective spaces

In this paper, we determine which blow-ups X of P n at general points are log Fano, that is, when there exists an effective Q-divisor Δ such that − ( K X + Δ ) is ample and the pair ( X , Δ ) is klt. For these blow-ups, we produce explicit boundary divisors Δ making X log Fano.

Toric graph associahedra and compactifications of $$M_{0,n}$$

To any graph G, one can associate a toric variety $$X(\mathcal {P}G)$$X(PG), obtained as a blowup of projective space along coordinate subspaces corresponding to connected subgraphs of G. The polytopes of these toric varieties are the graph associahedra, a class of polytopes that includes the permutohedron, associahedron, and stellahedron. We show that the space $$X(\mathcal {P}{G})$$X(PG) is isomorphic to a Hassett compactification of $$M_{0,n}$$M0,n precisely when G is an iterated cone over a discrete set. This may be viewed as a generalization of the well-known fact that the Losev---Manin moduli space is isomorphic to the toric variety associated with the permutohedron.