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 |
| _version_ | 1797219370780327936 |
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| author | Izzet Coskun Eric Larson Isabel Vogt |
| author_facet | Izzet Coskun Eric Larson Isabel Vogt |
| author_sort | Izzet Coskun |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T12:32:34Z |
| format | Article |
| id | doaj.art-1cd534a73df34452898100345c39cc99 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-24T12:32:34Z |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-1cd534a73df34452898100345c39cc992024-04-08T02:09:17ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.21Generic Beauville’s ConjectureIzzet Coskun0https://orcid.org/0000-0003-0775-5783Eric Larson1https://orcid.org/0000-0002-8379-9879Isabel Vogt2https://orcid.org/0000-0003-1152-9244Department of Mathematics, Statistics, and CS, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607, United States; E-mail:Department of Mathematics, Brown University, 151 Thayer Street, Providence, RI 02912, United States; E-mail:Department of Mathematics, Brown University, 151 Thayer Street, Providence, RI 02912, United StatesLet $\alpha \colon X \to Y$ 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.https://www.cambridge.org/core/product/identifier/S2050509424000215/type/journal_article14H6014D20 |
| spellingShingle | Izzet Coskun Eric Larson Isabel Vogt Generic Beauville’s Conjecture Forum of Mathematics, Sigma 14H60 14D20 |
| title | Generic Beauville’s Conjecture |
| title_full | Generic Beauville’s Conjecture |
| title_fullStr | Generic Beauville’s Conjecture |
| title_full_unstemmed | Generic Beauville’s Conjecture |
| title_short | Generic Beauville’s Conjecture |
| title_sort | generic beauville s conjecture |
| topic | 14H60 14D20 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424000215/type/journal_article |
| work_keys_str_mv | AT izzetcoskun genericbeauvillesconjecture AT ericlarson genericbeauvillesconjecture AT isabelvogt genericbeauvillesconjecture |