Picard bundles and the degree of irrationality of Jacobians
Federico Moretti, Andr\'es Rojas

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 , we study some positivity properties of (twisted) rank- Picard bundles on the -fold symmetric product. As an application, we prove that the degree of irrationality of any genus Jacobian is bounded from above by .
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