Punctual characterization of the unitary flat bundle of weight one PVHS and application to families of curves

IF 0.6 4区 数学 Q3 MATHEMATICS
Víctor González-Alonso, Sara Torelli
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引用次数: 0

Abstract

In this paper we consider the problem of pointwise determining the fibres of the flat unitary subbundle of a PVHS of weight one. Starting from the associated Higgs field, and assuming the base has dimension $1$, we construct a family of (smooth but possibly non-holomorphic) morphisms of vector bundles with the property that the intersection of their kernels at a general point is the fibre of the flat subbundle. We explore the first one of these morphisms in the case of a geometric PVHS arising from a family of smooth projective curves, showing that it acts as the cup-product with some sort of"second-order Kodaira-Spencer class"which we introduce, and check in the case of a family of smooth plane curves that this additional condition is non-trivial.
重一PVHS的酉平丛的穿刺特征及其在曲线族中的应用
本文研究了权为1的PVHS平面酉子束的纤维的点确定问题。从相关的希格斯场出发,假设基维为$1$,我们构造了向量束的一组(光滑但可能是非全纯的)态射,其性质是它们的核在一般点的交点是平坦子束的纤维。我们在光滑投影曲线族产生的几何PVHS的情况下探讨了这些态射中的第一个,表明它与我们引入的某种“二阶Kodaira-Spencer类”起杯积的作用,并检查了光滑平面曲线族的情况下这个附加条件是非平凡的。
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
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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