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ON MAXIMALLY FROBENIUS DESTABILISED VECTOR BUNDLES

Part of: Families, fibrations Curves Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  04 January 2019

LINGGUANG LI Open the ORCID record for LINGGUANG LI [Opens in a new window]
LINGGUANG LI*
Affiliation:
School of Mathematical Sciences, Tongji University, Shanghai, PR China email LiLg@tongji.edu.cn
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Abstract

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Let $X$ be a smooth projective curve of genus $g\geq 2$ over an algebraically closed field $k$ of characteristic $p>0$. We show that for any integers $r$ and $d$ with $0<r<p$, there exists a maximally Frobenius destabilised stable vector bundle of rank $r$ and degree $d$ on $X$ if and only if $r\mid d$.

Keywords

vector bundlemoduli spaceFrobenius morphism

MSC classification

Primary: 14H60: Vector bundles on curves and their moduli
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles 14D22: Fine and coarse moduli spaces 14G17: Positive characteristic ground fields

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 195 - 202
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported by the National Natural Science Foundation of China (Grant No. 11501418) and the Shanghai Sailing Program (15YF1412500).

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