A geometrical argument for a theorem of G. E. Welters (Q1818945)
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scientific article; zbMATH DE number 1384889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A geometrical argument for a theorem of G. E. Welters |
scientific article; zbMATH DE number 1384889 |
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A geometrical argument for a theorem of G. E. Welters (English)
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13 June 2000
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The existence of a one parameter family of trisecants to the Kummer variety of an indecomposable principally polarized abelian variety characterizes Jacobians. This result was first proved by \textit{R. C. Gunning} [Invent. Math. 66, 377-389 (1982; Zbl 0485.14009)] under additional hypotheses. Then \textit{G. E. Welters} [Ann. Math., II. Ser. 120, 497-504 (1984; Zbl 0574.14027) and Indag. Math. 45, 501-520 (1983; Zbl 0542.14029)] removed the additional hypotheses and considered the degenerate cases. In this note we provide a short geometrical argument for the inflectionary case.
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trisecants to the Kummer variety
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principally polarized abelian variety
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Jacobians
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0.8846089839935303
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0.8685269951820374
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0.8577433824539185
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