About: Fay's trisecant identity

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In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by Fay . Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties.

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  • In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by Fay . Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties. The name "trisecant identity" refers to the geometric interpretation given by , p.3.219), who used it to show that the Kummer variety of a genus g Riemann surface, given by the image of the map from the Jacobian to projective space of dimension 2g – 1 induced by theta functions of order 2, has a 4-dimensional space of trisecants. (en)
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  • 34672901 (xsd:integer)
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  • 2897 (xsd:nonNegativeInteger)
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  • 1030764254 (xsd:integer)
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  • John David Fay (en)
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  • Fay (en)
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  • chapter 3, page 34, formula 45 (en)
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  • 1973 (xsd:integer)
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  • In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by Fay . Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties. (en)
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  • Fay's trisecant identity (en)
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