{"title":"Picard Groups of Spectral Varieties and Moduli of Higgs Sheaves","authors":"Xiaoyu Su, Bin Wang","doi":"arxiv-2409.10296","DOIUrl":null,"url":null,"abstract":"We study moduli spaces of Higgs sheaves valued in line bundles and the\nassociated Hitchin maps on surfaces. We first work out Picard groups of generic\n(very general) spectral varieties which holds for dimension of at least 2,\ni.e., a Noether--Lefschetz type theorem for spectral varieties. We then apply\nthis to obtain a necessary and sufficient condition for the non-emptyness of\ngeneric Hitchin fibers for surfaces cases. Then we move on to detect the\ngeometry of the moduli spaces of Higgs sheaves as the second Chern class\nvaries.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10296","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.