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

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.

17 pages, comments are very welcome

References in corpus (3)

• Donaldson-Thomas invariants via microlocal geometry
• The Tanaka-Thomas's Vafa-Witten invariants via surface Deligne-Mumford stacks
• The Vafa-Witten invariants via surface Deligne-Mumford stacks and S-duality

Cited by in corpus (1)

• Twisted sheaves and $\mathrm{SU}(r)/{\mathbb{Z}}_r$ Vafa-Witten theory