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April, 2021 A Desingularization of the Moduli Space of Rank 2 Higgs Bundles over a Curve
Sang-Bum Yoo
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Taiwanese J. Math. 25(2): 257-301 (April, 2021). DOI: 10.11650/tjm/200901


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 $\mathbf{K}$.


First of all I wish to thank my supervisor Young-Hoon Kiem for suggesting problem, and for his help and encouragement. I am grateful to Conjeevaram Srirangachari Seshadri for his inspiring papers [20, 21]. I also thank Insong Choe for useful comments.


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Sang-Bum Yoo. "A Desingularization of the Moduli Space of Rank 2 Higgs Bundles over a Curve." Taiwanese J. Math. 25 (2) 257 - 301, April, 2021.


Received: 28 May 2019; Revised: 27 January 2020; Accepted: 2 September 2020; Published: April, 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.11650/tjm/200901

Primary: 14D15 , 14D22 , 14E05 , 14E15

Keywords: desingularization , Higgs bundle , parabolic Higgs bundle , specialization of $M(2)$

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

Vol.25 • No. 2 • April, 2021
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