1. Hitchin–Mochizuki morphism, opers and Frobenius-destabilized vector bundles over curves.
- Author
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Joshi, Kirti and Pauly, Christian
- Subjects
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MORPHISMS (Mathematics) , *FROBENIUS algebras , *VECTOR bundles , *CURVES , *STATISTICAL smoothing , *PROJECTIVE curves - Abstract
Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0 . For p > r ( r − 1 ) ( r − 2 ) ( g − 1 ) we construct an atlas for the locus of all Frobenius-destabilized bundles of rank r (i.e. we construct all Frobenius-destabilized bundles of rank r and degree zero up to isomorphism). This is done by exhibiting a surjective morphism from a certain Quot-scheme onto the locus of stable Frobenius-destabilized bundles. Further we show that there is a bijective correspondence between the set of stable vector bundles E over X such that the pull-back F ⁎ ( E ) under the Frobenius morphism of X has maximal Harder–Narasimhan polygon and the set of opers having zero p -curvature. We also show that, after fixing the determinant, these sets are finite, which enables us to derive the dimension of certain Quot-schemes and certain loci of stable Frobenius-destabilized vector bundles over X . The finiteness is proved by studying the properties of the Hitchin–Mochizuki morphism; an alternative approach to finiteness has been realized in [3] . In particular we prove a generalization of a result of Mochizuki to higher ranks. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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