Geodesic
Opers of higher types, Quot-schemes and Frobenius instability loci
Épijournal de Géométrie Algébrique, Tome 4 (2020)

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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 quot;maximal quot; 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. 
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     author = {Joshi, Kirti and Pauly, Christian},
     title = {Opers of higher types, {Quot-schemes} and {Frobenius} instability loci},
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Joshi, Kirti; Pauly, Christian. Opers of higher types, Quot-schemes and Frobenius instability loci. Épijournal de Géométrie Algébrique, Tome 4 (2020). doi: 10.46298/epiga.2020.volume4.5721

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