相关论文: Semipositivity theorem for reducible algebraic fib…

By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of non-uniruled polarized varieties.

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive…

We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial…

We give a new proof of a version of the main theorem of the previous paper in the series about embedding of an algebraic system into ultraproducts.

We prove a factorization theorem of generalized functions for moduli spaces of semistable parabolic bundles of any rank.

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…

This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space'' and its rational powers. Positive spaces are 1-dimensional ``semi-vector…

We obtain a version of the theorem of the square and a local structure result for actions of connected algebraic groups on seminormal varieties in characteristic 0, and arbitrary varieties in positive characteristics.

We investigate the positivity and extension of invertible sheaves on group homogeneous spaces over coherent bases. Bypassing the failure of standard limit arguments and the classical Weil--Cartier correspondence, we develop a valuative…

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…

In this article, we prove an extension property of semipositively metrized ample invertible sheaves on a projective scheme over a complete non-archimedean valued field. As an application, we establish a Nakai-Moishezon type criterion for…

We discuss the local freeness and the numerical semipositivity of direct images of relative pluricanonical bundles for surjective morphisms between smooth projective varieties with connected fibers. We give a desirable semipositivity…

The main goal of this paper is to prove the following theorem: Let $\frak k$ be an $\frak {sl}_2$-subalgebra of a semisimple Lie algebra $\frak g$, none of whose simple factors is of type $A1$. Then there exists a positive integer $b(\frak…

Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic group to a ramified cover. A version of Bertini Theorem in this context is also obtained.