谱变的皮卡群和希格斯剪切的模数

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-16 DOI:arxiv-2409.10296

Xiaoyu Su, Bin Wang

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引用次数: 0

摘要

我们研究线束中估值的希格斯剪的模空间以及曲面上相关的希钦映射。我们首先计算了一般（非常一般）谱变的皮卡群，它在维数至少为 2 时成立，即谱变的诺特--勒夫谢茨（Noether--Lefschetz）型定理。然后，我们应用这个定理得到了表面情况下一般希氏纤维非空的必要条件和充分条件。然后，我们继续探测希格斯剪切的模空间的几何性质，因为第二切恩类会发生变化。

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Picard Groups of Spectral Varieties and Moduli of Higgs Sheaves

We study moduli spaces of Higgs sheaves valued in line bundles and the associated Hitchin maps on surfaces. We first work out Picard groups of generic (very general) spectral varieties which holds for dimension of at least 2, i.e., a Noether--Lefschetz type theorem for spectral varieties. We then apply this to obtain a necessary and sufficient condition for the non-emptyness of generic Hitchin fibers for surfaces cases. Then we move on to detect the geometry of the moduli spaces of Higgs sheaves as the second Chern class varies.

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arXiv - MATH - Algebraic Geometry

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