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In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by Fay (, chapter 3, page 34, formula 45). Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties.

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  • 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 (, chapter 3, page 34, formula 45). Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties.
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  • chapter 3, page 34, formula 45
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  • John David Fay
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  • Fay
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  • In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by Fay (, chapter 3, page 34, formula 45). 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.
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