Frobenius-unstable bundles and p-curvature

Details Frobenius-unstable bundles and p-curvature Frobenius-unstable bundles and p-curvature

2004-09-16

arxiv.org/abs/math/0409266v1

Mathematics

Algebraic Geometry

32 pages. Contents of Chapters III and VI of PhD thesis, Massachusetts Institute of Technology, 2004

Scientific paper

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 math.AG/0409145 and math.AG/0407445. We also apply our explicit formulas to give a new description of the strata of curves of genus 2 of different p-rank.

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