Generic Beauville's Conjecture

Izzet Coskun; Eric Larson; Isabel Vogt

Generic Beauville's Conjecture

Algebraic Geometry 2023-07-11 v1

Authors: Izzet Coskun , Eric Larson , Isabel Vogt

Abstract

Let $\alpha: X \to Y$ 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

vector bundles vector bundles and cohomology algebraic curves

Cite

@article{arxiv.2307.04730,
  title  = {Generic Beauville's Conjecture},
  author = {Izzet Coskun and Eric Larson and Isabel Vogt},
  journal= {arXiv preprint arXiv:2307.04730},
  year   = {2023}
}

Related papers

View all related →