Characterization Of Projective Spaces Research Articles

SNC Log Symplectic Structures on Fano Products

AbstractThis paper classifies Poisson structures with the reduced simple normal crossing divisor on a product of Fano varieties of Picard number 1. The characterization of even-dimensional projective spaces from the viewpoint of Poisson structures is given by Lima and Pereira. In this paper, we generalize the characterization of projective spaces to any dimension.

Higher codimensional alpha invariants and characterization of projective spaces

We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable [Formula: see text]-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano manifolds in terms of higher codimensional alpha invariants. Our results demonstrate the relation between alpha invariants of any codimension and volumes of Fano manifolds in the characterization of projective spaces.

Frobenius–Seshadri constants and characterizations of projective space

We introduce higher-order variants of the Frobenius-Seshadri constant due to Musta\c{t}\u{a} and Schwede, which are defined for ample line bundles in positive characteristic. These constants are used to show that Demailly's criterion for separation of higher-order jets by adjoint bundles also holds in positive characteristic. As an application, we give a characterization of projective space using Seshadri constants in positive characteristic, which was proved in characteristic zero by Bauer and Szemberg. We also discuss connections with other characterizations of projective space.

Characterization of projective spaces by Seshadri constants

We prove that an n-dimensional complex projective variety is isomorphic to {mathbb {P}}^n if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n. We also classify complex projective varieties with Seshadri constants equal to n.

Characterizations of projective spaces and hyperquadrics

In this paper we prove that if the r-th tensor power of the tangent bundle of a smooth projective variety X contains the determinant of an ample vector bundle of rank at least r, then X is isomorphic either to a projective space or to a smooth quadric hypersurface.

A Remark on Characterizations of Projective Spaces among Singular Varieties

Let X be a projective variety of dimension n ≥ 2 with at worst log-terminal singularities and let \(E \subseteq T_X\) be an ample vector bundle of rank r. By partially extending previous results due to Andreatta and Wiśniewski in the smooth case, we prove that if r = n then \(X \cong {\mathbb{P}}^n\), while if r = n − 1 and X has only isolated singularities, then either \(X \cong {\mathbb{P}}^n\) or n = 2 and X is the quadric cone Q 2.

Note on Characterization of Projective Spaces

We prove a numerical characterization of ℙn for varieties with at worst isolated local complete intersection quotient singularities. In dimension 3, we prove such a numerical characterization of ℙ3 for normal ℚ-Gorenstein projective varieties.

Rational curves of minimal degree and characterizations of projective spaces

In this paper we investigate complex uniruled varieties X whose rational curves of minimal degree satisfy a special property. Namely, we assume that the tangent directions to such curves at a general point x ∈ X form a linear subspace of TxX. As a first application of our main result, we give a unified geometric proof of Mori's, Wahl's, Campana-Peternell's and Andreatta-Wiśniewski's characterizations of Open image in new window. We also give a characterization of products of projective spaces in terms of the geometry of their families of rational curves of minimal degree.

A Characterization of Projective Spaces by a Set of Planes

This note deals with the following question: How many planes of a linear space (P,\(\mathfrak{L}\)) must be known as projective planes to ensure that (P,\(\mathfrak{L}\)) is a projective space? The following answer is given: If for any subset M of a linear space (P,\(\mathfrak{L}\)) the restriction (M,\(\mathfrak{L}\))(M)) is locally complete, and if for every plane E of (M,\(\mathfrak{L}\)(M)) the plane \(\bar E\) generated by E is a projective plane, then (P,\(\mathfrak{L}\)) is a projective space (cf. 5.6). Or more generally: If for any subset M of P the restriction (M,\(\mathfrak{L}\)(M)) is locally complete, and if for any two distinct coplanar lines G1, G2 ∈ \(\mathfrak{L}\) (M) the lines \(\bar G_1 ,\bar G_2 \varepsilon \mathfrak{L}\) generated by G1, G2 have a nonempty intersection and \(\overline {G_1 \cup {\text{ }}G_2 }\) satisfies the exchange condition, then (P,\(\mathfrak{L}\)) is a generalized projective space.

A characterization of projective spaces in terms of $h$-enclosability

A characterization of projective spaces in terms of $h$-enclosability