Birationality of moduli spaces of twisted 1"> \(\mathrm {U}(p,q)\) -Higgs bundles

详细信息    查看全文

• 作者：Peter B. Gothen ; Azizeh Nozad
• 关键词：Higgs bundles ; Quiver bundles ; Indefinite unitary group ; Birationality of moduli
• 刊名：Revista Matemática Complutense
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：30
• 期：1
• 页码：91-128
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebra; Analysis; Applications of Mathematics; Geometry; Topology;
• 出版者：Springer Milan
• ISSN：1988-2807
• 卷排序：30

文摘

A \(\mathrm {U}(p,q)\)-Higgs bundle on a Riemann surface (twisted by a line bundle) consists of a pair of holomorphic vector bundles, together with a pair of (twisted) maps between them. Their moduli spaces depend on a real parameter \(\alpha \). In this paper we study wall crossing for the moduli spaces of \(\alpha \)-polystable twisted \(\mathrm {U}(p,q)\)-Higgs bundles. Our main result is that the moduli spaces are birational for a certain range of the parameter and we deduce irreducibility results using known results on Higgs bundles. Quiver bundles and the Hitchin–Kobayashi correspondence play an essential role.