Opers of higher types, Quot-schemes and Frobenius instability loci - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Article Dans Une Revue Épijournal de Géométrie Algébrique Année : 2020

Opers of higher types, Quot-schemes and Frobenius instability loci

Résumé

In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$ over a smooth projective curve defined over an algebraically closed field of characteristic $p>0$. In a previous paper we identified the "maximal" Frobenius instability strata with opers (more precisely as opers of type $1$ in the terminology of the present paper) and related them to certain Quot-schemes of Frobenius direct images of line bundles. The main aim of this paper is to describe for any integer $q \geq 1$ a conjectural generalization of this correspondence between opers of type $q$ (which we introduce here) and Quot-schemes of Frobenius direct images of vector bundles of rank $q$. We also give a conjectural formula for the dimension of the Frobenius instability locus. Comment: 17 pages; Final version Epijournal de G'eom'etrie Alg'ebrique, Volume 4 (2020), Article Nr. 17

Dates et versions

hal-03526751 , version 1 (14-01-2022)

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Kirti Joshi, Christian Pauly. Opers of higher types, Quot-schemes and Frobenius instability loci. Épijournal de Géométrie Algébrique, 2020, Volume 4, ⟨10.46298/epiga.2020.volume4.5721⟩. ⟨hal-03526751⟩
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