On vector bundles destabilized by Frobenius pull-back

Joshi, Kirti ; Ramanan, S. ; Xia, Eugene Z. ; Yu, Jiu-Kang (2006) On vector bundles destabilized by Frobenius pull-back Compositio Mathematica, 142 (3). pp. 616-630. ISSN 0010-437X

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Official URL: http://journals.cambridge.org/abstract_S0010437X05...

Related URL: http://dx.doi.org/10.1112/S0010437X05001788


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.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Projective Curves; Characteristic p; Frobenius Morphism
ID Code:45163
Deposited On:25 Jun 2011 07:56
Last Modified:29 Jun 2011 12:37

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