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

epiga:5721 - Épijournal de Géométrie Algébrique, December 8, 2020, Volume 4 -
Opers of higher types, Quot-schemes and Frobenius instability loci

Authors: Kirti Joshi ; Christian Pauly

    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
    Accepted on: September 13, 2020
    Submitted on: August 28, 2019
    Keywords: Mathematics - Algebraic Geometry

    Linked publications - datasets - softwares

    Source : ScholeXplorer IsRelatedTo ARXIV 1612.08213
    Source : ScholeXplorer IsRelatedTo DOI 10.1090/tran/7737
    Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1612.08213
    • 1612.08213
    • 10.48550/arxiv.1612.08213
    • 10.1090/tran/7737
    Frobenius Stratification of Moduli Spaces of Rank $3$ Vector Bundles in Characteristic $3$, I

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