On the construction of moduli stack of projective Higgs bundles over\n surfaces

2019/11/01 by Yunfeng Jiang, Jiang, Yunfeng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1911.00250

openalex publication_date 2019/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the construction of M. Lieblich for the compactification of the\nmoduli stack of PGL_r-bundles on algebraic spaces to the moduli stack of\nTanaka-Thomas PGL_r-Higgs bundles on algebraic schemes. The method we use is\nthe moduli stack of Higgs version of Azumaya algebras. In the case of smooth\nsurfaces, we obtain a virtual fundamental class on the moduli stack of\n PGL_r-Higgs bundles. An application to the Vafa-Witten invariants is\ndiscussed.\n

Citations

• Donaldson-Thomas invariants via microlocal geometry

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