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arXiv · 2403.16625

A perfect obstruction theory for SU(2)-Higgs pairs

Simon Schirren
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Abstract

We present a new method for constructing virtual cycles for rank-2 Higgs sheaves $(E,ϕ)$ on a smooth projective surface $S$. Using this, we redefine the $\mathbf{SU}(2)$-perfect obstruction theory previously constructed by Tanaka-Thomas. The key step in our construction involves modifying the $\mathbf{C}^\times$-localisation formula of Graber-Pandharipande by replacing the torus action with an involution $(E,ϕ) \mapsto (E^*,-ϕ^*)$.

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Simon Schirren. 2025-04-16. A perfect obstruction theory for SU(2)-Higgs pairs. https://arxiv.org/abs/2403.16625

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