Related papers: On semipositivity, injectivity and vanishing theor…

In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it ``skew semi-derivation". Further, we present a study of the conditions under which this type of multiplicative…

A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…

The goal of this paper is to provide some basic structure information on derivations in finite semirings.

The purpose of this note is to give a survey of the algebraic properties of multiplier ideals, and illustrate some of their applications to classical projective geometry.

This is a brief overview of some applications of the ideas of abstract convexity to the upper semilattices of gauges in finite dimensions.

An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.

After the introduction in 1994, by Okabe and Matsuda, of the notion of semistar operation, many authors have investigated different aspects of this general and powerful concept. A natural development of the recent work in this area leads to…

In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2,2,...,2).

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed…

The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced…

We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning homological projective duality. Then we introduce…

In this article we survey some of the recent developments in the structure theory of set addition.

This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…

We prove a new vanishing theorem generalizing that of Le Potier for Schur functors of a vector bundle.

Some diophantine aspects of projective toric varieties: We present several faces of projective toric varieties, of interest from the point of view of diophantine geometry. We make explicit the theory on a number of meaningful examples and…

We give a new proof of vanishing result of Esnault for the cohomology of constructible sheaves in the tower of ``mock'' Frobenius covers of projective space. The key idea is to use (a global form of) the perversity of nearby cycles.

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

In this paper, we introduce and study e-injective semimodules, in particular over additively idempotent semirings. We completely characterize semirings all of whose semimodules are e-injective, describe semirings all of whose projective…

Axions and other very light axion-like particles appear in many extensions of the Standard Model, and are leading candidates to compose part or all of the missing matter of the Universe. They also appear in models of inflation, dark…

A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the $E_1$-degeneration of Hodge to de…