相关论文: Compactifying normal algebraic spaces

We construct a smooth symmetric compactification of the space of all labeled tetrahedra in P^3.

We give a revision of the proof of a Mazur-Ulam theorem for generalized gyrovector spaces given in the paper "Generalized gyrovector spaces and a Mazur-Ulam theorem" published in Publ. Math. Debrecen, 87 (2015), 393--413.

This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces,…

The purpose of this note is to advertise an elegant algorithmic proof for the Jordan--Chevalley decomposition of a matrix, following and (slightly) revising the discussion of Couty, Esterle und Zarouf (2011). The basic idea of that method…

We construct an Asplund Banach space $\mathcal{X}$ with a norming Marku\v{s}evi\v{c} basis such that $\mathcal{X}$ is not weakly compactly generated. This solves a long-standing open problem from the early nineties, originally due to Gilles…

We study compact spaces which are obtained from metric compacta by iterating the operation of inverse limit of continuous sequences of retractions. We denote this class by R. Allowing continuous images in the definition of class R, one…

We prove a coordinatization theorem for unital alternative algebras containing 2 x 2 matrix algebra with the same identity element 1. This solves an old problem announced by Nathan Jacobson on the description of alternative algebras…

We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of…

A topological space $X$ is called $\Cal A$-real compact, if every algebra homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$, where $\Cal A$ is an algebra of continuous functions. Our main interest lies on…

This essay points to many of the interesting ramifications of Margulis' arithmeticity theorem, the superrigidity theorem, and normal subgroup theorem. We provide some history and background, but the main goal is to point to interesting open…

A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this paper we discuss the possible degenerations of these abelian varieties, and thus give a description of…

We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the…

We give an introduction to the compactification of the moduli space of surfaces of general type introduced by Koll\'ar and Shepherd-Barron and generalized to the case of surfaces with a divisor by Alexeev. The construction is an application…

The class of $L\Sigma(\leq\omega)$-spaces was introduced in 2006 by Kubi\'s, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindel\"of $\Sigma$-spaces. Compact $L\Sigma(\leq\omega)$-spaces were…

Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…

We present an algorithm for obtaining the matter content of effective six-dimensional theories resulting from compactification of F-theory on elliptic Calabi-Yau threefolds which are hypersurfaces in toric varieties. The algorithm allows us…

Let $R_4$ be the space of rational plane curves of degree $4$. In this paper, we obtain a sheaf theoretic compactification of $R_4$ via the space of $\alpha$-semistable pairs on $\mathbb{P}^2$ and its birational relations through…

We describe two geometrically meaningful compactifications of the moduli space of elliptic K3 surfaces via stable slc pairs, for two different choices of a polarizing divisor, and show that their normalizations are two different toroidal…

In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed…

The aim of this paper is to construct the parabolic version of the Donaldson--Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing…