Generic Beauville’s Conjecture
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000215/type/journal_article |
| Summary: | 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. |
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| ISSN: | 2050-5094 |