曲面上大量曲线的霍奇结构的一般无穷小变化

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-06-04 DOI:10.1002/mana.12028

Víctor González-Alonso, Sara Torelli

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引用次数: 0

摘要

给定光滑投影曲面内的光滑投影复曲线，人们可以问当曲线在曲面内移动时它的霍奇结构是如何变化的。在本文中，我们发展了一个一般理论来研究这个问题在样本曲线情况下的无穷小版本。然后，我们可以应用该机制来证明在p1 × p1 $\mathbb {P}^1\乘以\mathbb {P}^1$中样本曲线的一般变形的无穷小变化的Hodge结构是同构的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

General infinitesimal variations of the Hodge structure of ample curves in surfaces

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General infinitesimal variations of the Hodge structure of ample curves in surfaces

Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper, we develop a general theory to study the infinitesimal version of this question in the case of ample curves. We can then apply the machinery to show that the infinitesimal variation of the Hodge structure of a general deformation of an ample curve in $P^{1} \times P^{1}$ is an isomorphism.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index