Upper bounds on the genus of hyperelliptic Albanese fibrations
Let S be a minimal irregular surface of general type, whose Albanese map induces a hyperelliptic fibration $f:\,S \to B$ of genus g. We prove a quadratic upper bound on the genus g (i.e., $g\leq h\big (\chi (\mathcal {O}_S)\big )$ , where h is a quadratic function). We also construct ex...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S205050942500043X/type/journal_article |
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| Summary: | Let S be a minimal irregular surface of general type, whose Albanese map induces a hyperelliptic fibration
$f:\,S \to B$
of genus g. We prove a quadratic upper bound on the genus g (i.e.,
$g\leq h\big (\chi (\mathcal {O}_S)\big )$
, where h is a quadratic function). We also construct examples showing that the quadratic upper bounds cannot be improved to linear ones. In the special case when
$p_g(S)=q(S)=1$
, we show that
$g\leq 14$
. |
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| ISSN: | 2050-5094 |