On vector bundles destabilized by Frobenius pull-back

Kirti Joshi, S. Ramanan, Eugene Z. Xia, Jiu Kang Yu

研究成果: Article同行評審

27 引文 斯高帕斯(Scopus)

摘要

Let X be a smooth projective curve of genus g > 1 over an algebraically closed field of positive characteristic. This paper is a study of a natural stratification, defined by the absolute Frobenius morphism of X, on the moduli space of vector bundles. In characteristic two, there is a complete classification of semi-stable bundles of rank 2 which are destabilized by Frobenius pull-back. We also show that these strata are irreducible and obtain their respective dimensions. In particular, the dimension of the locus of bundles of rank two which are destabilized by Frobenius is 3g-4. These Frobenius destabilized bundles also exist in characteristics two, three and five with ranks 4, 3 and 5, respectively. Finally, there is a connection between (pre)-opers and Frobenius destabilized bundles. This allows an interpretation of some of the above results in terms of pre-opers and provides a mechanism for constructing Frobenius destabilized bundles in large characteristics.

原文English
頁(從 - 到)616-630
頁數15
期刊Compositio Mathematica
142
發行號3
DOIs
出版狀態Published - 2006

All Science Journal Classification (ASJC) codes

  • 代數與數理論

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