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Bibliographic Details
Main Author: Schirren, Simon
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.16625
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author Schirren, Simon
author_facet Schirren, Simon
contents 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 $(E,ϕ) \mapsto (E^*,-ϕ^*)$.
format Preprint
id arxiv_https___arxiv_org_abs_2403_16625
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A perfect obstruction theory for SU(2)-Higgs pairs
Schirren, Simon
Algebraic Geometry
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 $(E,ϕ) \mapsto (E^*,-ϕ^*)$.
title A perfect obstruction theory for SU(2)-Higgs pairs
topic Algebraic Geometry
url https://arxiv.org/abs/2403.16625