Picard bundles and the degree of irrationality of Jacobians

TL;DR

This paper investigates positivity properties of Picard bundles on symmetric products of curves and establishes an upper bound of 2^g for the degree of irrationality of genus g Jacobians.

Contribution

It introduces new positivity results for Picard bundles and provides a novel upper bound for the degree of irrationality of Jacobians.

Findings

Bound of 2^g for the degree of irrationality of genus g Jacobians.

Positivity properties of twisted rank-g Picard bundles on symmetric products.

Application of bundle positivity to geometric bounds.

Abstract

For a smooth projective curve of genus $g$, we study some positivity properties of (twisted) rank-$g$ Picard bundles on the $g$-fold symmetric product. As an application, we prove that the degree of irrationality of any genus $g$ Jacobian is bounded from above by $2^g$.