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arXiv · 2605.18469

Picard bundles and the degree of irrationality of Jacobians and Pryms

Federico Moretti·Andrés Rojas
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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 $2^g$, and the degree of irrationality of any $(g-1)$-dimensional Prym variety is bounded from above by $2^{2g-3}$.

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Federico Moretti, Andrés Rojas. 2026-05-18. Picard bundles and the degree of irrationality of Jacobians and Pryms. https://arxiv.org/abs/2605.18469

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