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Transactions of the American Mathematical Society

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Frobenius stratification of moduli spaces of rank $ 3$ vector bundles in positive characteristic $ 3$, I


Author: Lingguang Li
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14H60, 14G17; Secondary 14D20, 14D22
DOI: https://doi.org/10.1090/tran/7737
Published electronically: December 28, 2018
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Abstract: Let $ X$ be a smooth projective curve of genus $ g\geq 2$ over an algebraically closed field $ k$ of characteristic $ p>0$, and let $ F_X:X\rightarrow X$ be the absolute Frobenius morphism. Let $ \mathfrak{M}^s_X(r,d)$ be the moduli space of stable vector bundles of rank $ r$ and degree $ d$ on $ X$. We study the Frobenius stratification of $ \mathfrak{M}^s_X(3,0)$ in terms of Harder-Narasimhan polygons of Frobenius pull backs of stable vector bundles and obtain the irreducibility and dimension of each nonempty Frobenius stratum in the case in which $ (p,g)=(3,2)$.


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Additional Information

Lingguang Li
Affiliation: School of Mathematical Sciences, Tongji University, Shanghai, People’s Republic of China
Email: LiLg@tongji.edu.cn

DOI: https://doi.org/10.1090/tran/7737
Keywords: Vector bundle, moduli space, Frobenius morphism, stratification
Received by editor(s): April 25, 2017
Received by editor(s) in revised form: May 13, 2018, and October 22, 2018
Published electronically: December 28, 2018
Additional Notes: This work was supported by the National Natural Science Foundation of China (Grant No. 11501418), the Shanghai Sailing Program, and the Program for Young Excellent Talents in Tongji University.
Dedicated: Dedicated to the memory of Professor Michel Raynaud
Article copyright: © Copyright 2018 American Mathematical Society