Prym varieties of triple cyclic covers (Q1092971)
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scientific article; zbMATH DE number 4021341
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Prym varieties of triple cyclic covers |
scientific article; zbMATH DE number 4021341 |
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Prym varieties of triple cyclic covers (English)
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1988
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Prym varieties associated to unramified triple cyclic covers are studied. We construct the Prym map from the moduli space of curves of genus \(g\) with such a cover to a certain moduli space of abelian varieties of dimension 2g-2 with a non-principal polarization and with an automorphism of order three. The main theorem is that for \(g=4\) this Prym map is generically finite of degree \(16;\) moreover, the general fiber carries a \((16_ 6)\) Kummer structure.
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Prym varieties
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unramified triple cyclic covers
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moduli space
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non- principal polarization
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automorphism
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