Related papers: Lefschetz for local Picard groups

We generalize Koll\'ar's package (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles twisted by a multiplier ideal sheaf associated with an…

We establish a Lefschetz hyperplane theorem for the Berkovich analytifications of Jacobians of curves over an algebraically closed non-Archimedean field. Let $J$ be the Jacobian of a curve $X$, and let $W_d \subset J$ be the locus of…

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…

We prove that Local Fundamental Group Scheme satisfies the conditions of Lefschetz-Bott-Grothendieck.

For a certain class of abelian categories, we show how to make sense of the "Euler characteristic" of an infinite projective resolution (or, more generally, certain chain complexes that are only bounded above), by passing to a suitable…

We show that in positive characteristic special loci of deformation spaces of rank one $\ell$-adic local systems are quasilinear. From this we deduce the Hard Lefschetz theorem for rank one $\ell$-adic local systems and a generic vanishing…

In this paper we show some Lefschetz-type theorems for the effective cone of Hyperk\"ahler varieties. In particular we are able to show that the inclusion of any smooth ample divisor induces an isomorphism of effective cones. Moreover we…

We prove a relative version of the Picard-Lefschetz theorem, describing the variation of relative homology groups $H_d(Y_t \setminus A_t,B_t\setminus A_t)$ in the fibers of a smooth fiber bundle $Y \to T$ of complex manifolds with $A\cup B…

Let $L$ be a proper finite extension of the field of $p$-adic numbers and let $o\subset L$ be its integers, viewed as an abelian locally $L$-analytic group. Let $\hat{o}$ be the rigid analytic group variety parametrizing the locally…

We study the Lefschetz standard conjecture on a smooth complex projective variety X. In degree 2, we reduce it to a local statement concerning deformations of vector bundles on X. When X is hyperk\"ahler, we show that the existence of…

The monodromy action in the homology (generally with twisted coefficients) of complements of stratified complex analytic varieties depending on parameters is studied. For a wide class of local degenerations of such families (stratified…

The purpose of this paper is to give a proof of the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an…

In this paper we construct classifying localic categories and groupoids for various bundles equipped with logical structure. When these bundles are local homeomorphisms, we recover the localic groupoids that classify geometric theories,…

For a given complex projective variety, the existence of entire curves is strongly constrained by the positivity properties of the cotangent bundle. The Green-Griffiths-Lang conjecture stipulates that entire curves drawn on a variety of…

One version of the classical Lefschetz hyperplane theorem states that for $U \subset \mathbb P^n$ a smooth quasi-projective variety of dimension at least $2$, and $H \cap U$ a general hyperplane section, the resulting map on \'etale…

We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefschetz fixed-morphism theorem. In order to do so, we use the…

We compute the class groups of very general normal surfaces in complex projective three-space containing an arbitrary base locus $Z$, thereby extending the classic Noether-Lefschetz theorem (the case when $Z$ is empty). Our method is an…

We extend the group theoretic construction of local models of Pappas and Zhu to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive…

We introduce a new fundamental group scheme for varieties defined over an algebraically closed field of positive characteristic and we use it to study generalization of some of C. Simpson's results to positive characteristic. We also study…

We describe the standard and Leray filtrations on the cohomology groups with compact supports of a quasi projective variety with coefficients in a constructible complex using flags of hyperplane sections on a partial compactification of a…