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

Yunfeng Jiang

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

Algebraic Geometry 2019-11-04 v1

Authors: Yunfeng Jiang

Abstract

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

Keywords

moduli stack higgs bundles pgl_r-bundles azumaya algebras virtual fundamental class vafa-witten invariants

Cite

@article{arxiv.1911.00250,
  title  = {On the construction of moduli stack of projective Higgs bundles over surfaces},
  author = {Yunfeng Jiang},
  journal= {arXiv preprint arXiv:1911.00250},
  year   = {2019}
}

Comments

17 pages, comments are very welcome

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