Related papers: Semipositivity theorem for reducible algebraic fib…
We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…
We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra…
We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded $C_0$-semigroups on Hilbert spaces.
We prove that each semialgebraic subset of $\R^n$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving…
In this short article we provide a proof of the Iitaka conjecture for algebraic fiber spaces over abelian varieties.
We prove the abundance theorem for semi log canonical surfaces in positive characteristic.
Our aim is to construct fibrewise localizations in model categories. For pointed spaces, the general idea is to decompose the total space of a fibration as a diagram over the category of simplices of the base and replace it by the localized…
We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…
We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal…
We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.
Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies…
In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.
In this paper, we investigate semisimplicity of cellular algebras over positive characteristic fields. Our main result shows that the Frame number of cellular algebras characterizes semisimplicity of it. In a sense, this is a generalization…
This paper suggests an algebraic version of the theorem on the existence of eigenvectors for linear operators in abstract idempotent spaces. Earlier, the theorem on the existence of eigenvectors was only known for the cases of a free…
We propose a simple proof of the vertical half-space theorem for Heisenberg space.
We study affine semigroup rings as algebras over subsemigroup rings. From this relative viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup algebras is constructed. Such a construction is compared to…
This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis.…
We prove a semistable reduction theorem for principal bundles on curves in almost arbitrary characteristics. For exceptional groups we need some small explicit restrictions on the characteristic.
We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…