Frobenius-unstable bundles and $p$-curvature
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- by Brian Osserman PDF
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Abstract:
We use the theory of $p$-curvature of connections to analyze stable vector bundles of rank 2 on curves of genus 2 which pull back to unstable bundles under the Frobenius morphism. We take two approaches, first using explicit formulas for $p$-curvature to analyze low-characteristic cases, and then using degeneration techniques to obtain an answer for a general curve by degenerating to an irreducible rational nodal curve, and applying the results of additional works by the author. We also apply our explicit formulas to give a new description of the strata of curves of genus 2 of different $p$-rank.References
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Additional Information
- Brian Osserman
- Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
- MR Author ID: 722512
- Received by editor(s): September 17, 2004
- Received by editor(s) in revised form: November 11, 2005
- Published electronically: May 17, 2007
- Additional Notes: This paper was partially supported by fellowships from the National Science Foundation and Japan Society for the Promotion of Science.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 273-305
- MSC (2000): Primary 14H60
- DOI: https://doi.org/10.1090/S0002-9947-07-04218-3
- MathSciNet review: 2342003