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A desingularization of the moduli space ...
Yoo, Sang-Bum...

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A desingularization of the moduli space of rank 2 Higgs bundles over a curve by Yoo, Sang-Bum ( Author )
Lemonjar Open Access
Australian National University
04-08-2023
Let $X$ be a smooth complex projective curve of genus $g\geq 3$. Let $\mathbf{M}_2$ be the moduli space of semistable rank $2$ Higgs bundles with trivial determinant over $X$. We construct a desingularization $\mathbf{S}$ of $\mathbf{M}_2$ as a closed subvariety of a moduli space. We prove that $\mathbf{S}$ is a nonsingular variety containing the stable locus of $\mathbf{M}_2$ as an open dense subvariety. On the other hand, there is another desingularization $\mathbf{K}$ of $\mathbf{M}_2$ obtained from Kirwan's algorithm. We show that $\mathbf{S}$ can be obtained after two blow-downs of $\mathbf{K}$.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1310.7809
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