Hitchin-Mochizuki morphism, Opers and Frobenius-destabilized vector bundles over curves - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2015

Hitchin-Mochizuki morphism, Opers and Frobenius-destabilized vector bundles over curves

Résumé

Let X be a smooth projective curve of genus g >1 defined over an algebraically closed field k of characteristic p >0. For p sufficiently large (explicitly given in terms of r,g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of 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 a recent preprint by Chen and Zhu. In particular we prove a generalization of a result of Mochizuki to higher ranks.
Fichier principal
Vignette du fichier
Hit-Moc-final.pdf (374.47 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00442035 , version 1 (17-12-2009)
hal-00442035 , version 2 (16-05-2010)
hal-00442035 , version 3 (15-01-2015)

Identifiants

Citer

Kirti Joshi, Christian Pauly. Hitchin-Mochizuki morphism, Opers and Frobenius-destabilized vector bundles over curves. Advances in Mathematics, 2015, pp.39-75. ⟨hal-00442035v3⟩
331 Consultations
793 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More