Forum of Mathematics, Sigma (Jan 2024)

Generic Beauville’s Conjecture

  • Izzet Coskun,
  • Eric Larson,
  • Isabel Vogt

DOI
https://doi.org/10.1017/fms.2024.21
Journal volume & issue
Vol. 12

Abstract

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Let $\alpha \colon X \to Y$ be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under $\alpha $ is semistable if the genus of Y is at least $1$ and stable if the genus of Y is at least $2$ . We prove this conjecture if the map $\alpha $ is general in any component of the Hurwitz space of covers of an arbitrary smooth curve Y.

Keywords