Analytic semi-universal deformations in logarithmic complex geometry

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-02-24 DOI:10.1007/s12188-023-00264-y

Raffaele Caputo

引用次数: 1

Abstract

We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the analogous results in complex analytic geometry first independently proved by A. Douady and H. Grauert in the ’70. We follow Douady’s two steps process approach consisting of an infinite-dimensional construction of the deformation space followed by a finite-dimensional reduction.

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对数复几何中的解析半泛型变形

我们证明了每一个具有精细对数结构的紧致复解析空间和这些空间之间的每一个态射都允许半泛变形。这些结果推广了A.Douady和H.Grauert在70年代首次独立证明的复解析几何中的类似结果。我们遵循Douady的两步过程方法，包括变形空间的无限维构造和有限维简化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.