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

Yunfeng Jiang

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arXiv · 1911.00250

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

Yunfeng Jiang

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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.

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BibTeX RIS

Yunfeng Jiang. 2019-11-01. On the construction of moduli stack of projective Higgs bundles over surfaces. https://arxiv.org/abs/1911.00250

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