## Joshi, Kirti and Pauly, Christian - Opers of higher types, Quot-schemes and Frobenius instability loci

epiga:5721 - Épijournal de Géométrie Algébrique, December 8, 2020, Volume 4 - https://doi.org/10.46298/epiga.2020.volume4.5721
Opers of higher types, Quot-schemes and Frobenius instability loci

Authors: Joshi, Kirti and Pauly, Christian

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.

Volume: Volume 4
Published on: December 8, 2020
Submitted on: August 28, 2019
Keywords: Mathematics - Algebraic Geometry