Abstract
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 $\mathbf{K}$.
Acknowledgments
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.
Citation
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. https://doi.org/10.11650/tjm/200901
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