The Rank of the Cartier operator on cyclic covers of the projective line

TL;DR

This paper establishes a lower bound on the rank of the Cartier operator for Jacobian varieties of hyperelliptic and superelliptic curves, linking it to the genus of the curves.

Contribution

It provides a new lower bound on the Cartier operator's rank for specific classes of algebraic curves, advancing understanding of their geometric properties.

Findings

Lower bound on Cartier operator rank for hyperelliptic curves

Lower bound on Cartier operator rank for superelliptic curves

Enhanced understanding of Jacobian varieties in algebraic geometry

Abstract

We give a lower bound on the rank of the Cartier operator of Jacobian varieties of hyperelliptic and superelliptic curves in terms of their genus.