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arXiv · 2510.24531

A virtual structure for symplectic Higgs bundles

Simon Schirren
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Abstract

We define a perfect obstruction theory for a moduli of symplectic Higgs sheaves $(E,\phi)$ on projective surfaces $S$. Key to this is a minimality assumption on $\textrm{ch}(E)$ that forces all $E$ to be locally free. This might have implications to define a virtual count and $Sp(r)$-Vafa-Witten invariants.

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Simon Schirren. 2025-10-28. A virtual structure for symplectic Higgs bundles. https://arxiv.org/abs/2510.24531

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