Erschienen:
Cambridge University Press (CUP), 2024
Erschienen in:Forum of Mathematics, Sigma
Sprache:
Englisch
DOI:
10.1017/fms.2024.21
ISSN:
2050-5094
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title>
<jats:p>Let <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050509424000215_inline1.png" />
<jats:tex-math>
$\alpha \colon X \to Y$
</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050509424000215_inline2.png" />
<jats:tex-math>
$\alpha $
</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> is semistable if the genus of <jats:italic>Y</jats:italic> is at least <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050509424000215_inline3.png" />
<jats:tex-math>
$1$
</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> and stable if the genus of <jats:italic>Y</jats:italic> is at least <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050509424000215_inline4.png" />
<jats:tex-math>
$2$
</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>. We prove this conjecture if the map <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050509424000215_inline5.png" />
<jats:tex-math>
$\alpha $
</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> is general in any component of the Hurwitz space of covers of an arbitrary smooth curve <jats:italic>Y</jats:italic>.</jats:p>