Related papers: Classes de Chern des vari\'et\'es unir\'egl\'ees

This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic…

We show a degree formula for a type of orthogonal Deligne--Lusztig varieties and their Pl\"ucker embeddings. This is an analog of work of Li on a unitary case.

We extend Orlov's representability theorem on the equivalence of derived categories of sheaves to the case of smooth stacks associated to normal projective varieties with only quotient singularities.

We prove recent conjectures of Chern concerning nonnegativity of a certain q-series related to parity bias in integer partitions.

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

We discuss several numerical conditions for families of projective varieties or variations of Hodge structures.

The aim of this note is to use elementary methods to give a large class of examples of projective varieties $ Y \subseteq \mathbb{P}^d_k$ over a field $k$ with the property that $Y$ is not isomorphic to a hypersurface $H\subseteq…

Given a generic degree-2 cover of a genus 1 curve D by a non hyperelliptic genus 3 curve C over a field k of characteristic different from 2, we produce an explicit genus 2 curve X such that Jac(C) is isogenous to the product of Jac(D) and…

We give an example of a pair of projective symplectic varieties in arbitrarily large dimensions which are D-equivalent, L-equivalent, and birationally inequivalent.

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P^N and of its twists F(t) as polynomials in the Chern classes c_i(F), also giving algorithms for the computation. The employed…

We show various properties of smooth projective D-affine varieties. In particular, any smooth projective D-affine variety is algebraically simply connected and its image under a fibration is D-affine. In characteristic zero such D-affine…

We first construct closed spherical CR manifolds of dimension at least five having non-trivial first Chern class with real coefficients. We next prove a constraint on Chern classes with real coefficients of (not necessarily closed)…

Let $f:\, X\to Y$ be a semistable non-isotrivial family of $n$-folds over a smooth projective curve with discriminant locus $S \subseteq Y$ and with general fibre $F$ of general type. We show the strict Arakelov inequality…

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector…

The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…

Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This…

We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.

We use bisection to provide an algebraic proof that the Chern form on the convolution algebra of an \'etale groupoid is closed.