Related papers: Ample subvarieties and q-ample divisors

In this paper, we provide an alternative proof of Donaldson's almost-holomorphic section theorem and symplectic Lefschetz pencil theorem, through constructions of certain special kind of Donaldson-type sections of the line bundle based on…

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 prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…

The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these…

We study fundamental forms of algebraic varieties using the sheaves of principal parts of line bundles and establish a vanishing theorem for any order fundamental forms. We also give connection of fundamental forms with the higher order…

In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…

The goal of this paper is to show that there are strong relations between certain Monge-Amp\`ere integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles.…

We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and…

We investigate effectiveness and ampleness of adjoint divisors of the form $aL+bK_X$, where $L$ is a suitably positive line bundle on a smooth projective variety $X$ and $a,b$ are positive integers.

We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…

In this note, we propose a geometric analogue of Dirichlet's unit theorem on arithmetic varieties, that is, if X is a normal projective variety over a finite field and D is a pseudo-effective Q-Cartier divisor on X, does it follow that D is…

The goal of this work is to pursue the study of pseudo-effective line bundles and vector bundles. Our first result is a generalization of the Hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle. The Lefschetz…

In this note we study two features of submanifolds (subvarieties) with ample normal bundles in a compact K\"ahler manifold X. First, we study how algebraic X can be, i.e. we investigate the algebraic dimension. Second, we study curves with…

Given an effective Q-divisor D on a smooth complex variety, one can associate to D its multiplier ideal sheaf J(D), which measures in a somewhat subtle way the singularities of D. Because of their strong vanishing properties, these ideals…

The purpose of this note is to extend some classical results on quasi-projective schemes to the setting of derived algebraic geometry. Namely, we want to show that any vector bundle on a derived scheme admitting an ample line bundle can be…

Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^n$. As an application, we derive the classification of projective manifolds containing a…

The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms…

In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…

Let $(X, \Delta)$ be a projective klt three dimensional pair defined over an algebraically closed field characteristic larger than 5. Let $L$ be a nef and big line bundle on $X$ such that $L-K_X-\Delta$ is big and nef. We show that $L$ is…

We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.