Frobenius stratification of moduli spaces of rank $3$ vector bundles in positive characteristic $3$, I
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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 $(p,g)=(3,2)$.References
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Additional Information
- Lingguang Li
- Affiliation: School of Mathematical Sciences, Tongji University, Shanghai, People’s Republic of China
- MR Author ID: 1019070
- ORCID: 0000-0002-0205-6775
- Email: LiLg@tongji.edu.cn
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 5693-5711
- MSC (2010): Primary 14H60, 14G17; Secondary 14D20, 14D22
- DOI: https://doi.org/10.1090/tran/7737
- MathSciNet review: 4014291
Dedicated: Dedicated to the memory of Professor Michel Raynaud