霍奇束上度量的奇异性及其拓扑不变量

IF 1.7 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2016-11-09 DOI:10.14231/AG-2018-021

Dennis Eriksson, G. F. I. Montplet, Christophe Mourougane

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引用次数: 11

摘要

本文研究了复杂投影Calabi-Yau的退化，并研究了Hodge束和行列式束上L2、Quillen和BCOV度量的奇异性。在接近非光滑纤维的度量展开中的主导项和次主导项被证明与已知的奇点拓扑不变量有关，如极限Hodge结构、消失循环和对数正则阈值。在Quillen度规的情况下，我们还描述了更一般退化族的相应不变量。

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Singularities of metrics on Hodge bundles and their topological invariants

We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of L2, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibers are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds. We also describe corresponding invariants for more general degenerating families in the case of the Quillen metric.

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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.