Related papers: Koll\'ar--Nadel type vanishing theorem

Given a p-form defined on the smooth locus of a normal variety, and a resolution of singularities, we study the problem of extending the pull-back of the p-form over the exceptional set of the desingularization. For log canonical pairs and…

The classical Kodaira Vanishing Theorem states that Hi(X, {\omega}X \otimes L) = 0 for i > 0, where X is a smooth projective variety over C and L is an ample line bundle on X. We prove an analogous vanishing result under the assumption that…

Call a normal complex projective variety $X$ Koll\'ar-hyperbolic if any nonconstant map from a smooth projective curve to $X$ induces a nontrivial homomorphism of \'etale fundamental groups. Examples include (a) smooth varieties with finite…

We reconsider the Adler-Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin-Vilkovisky formalism and combining the dimensional-regularization technique with the…

We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques…

Let $L$ be a line bundle on a K3 or Enriques surface. We give a vanishing theorem for $H^1(L)$ that, unlike most vanishing theorems, gives necessary and sufficient geometrical conditions for the vanishing. This result is essential in our…

A cohomological vanishing property is proved for finitely supported ideals in an arbitrary d-dimensional regular local ring. (Such vanishing implies some refined Briancon-Skoda-type results, not otherwise known in mixed characteristic.) It…

In this work, we establish new analytical results which are required for the derivation of subtle properties of the members of two classes of the generalized Feller--Spitzer distributions introduced in our forthcoming paper.

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].

We study abstract versions of G\"odel's second incompleteness theorem and formulate generalizations of L\"ob's derivability conditions that work for logics weaker than the classical one. We isolate the role of contraction rule in G\"odel's…

We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…

We show that the mod $p$ cohomology of a simple Shimura variety treated in Harris-Taylor's book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we…

Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this note, we review some new and easy-to-use techniques to show…

We show that generic vanishing fails for singular varieties and in characteristic p>0.

We survey the classical results of the Dirichlet Approximation Theorem.

There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equation. The theorem describes the growth of the series…

We introduce and study a relative cancellation property for associative algebras. We also prove a characterization result for polynomial rings which partially answers a question of Kraft.

An algorithmic proof of the General N\'eron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case.

We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.

For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.