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In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by . 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 , 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 2''g'' – 1 induced by theta functions of order 2, has a 4-dimensional space of trisecants. ==Statement== Suppose that *''C'' is a compact Riemann surface *''g'' is the genus of ''C'' *θ is the Riemann theta function of ''C'', a function from C''g'' to C *''E'' is a prime form on ''C''×''C'' *''u'',''v'',''x'',''y'' are points of ''C'' *''z'' is an element of C''g'' *ω is a 1-form on ''C'' with values in C''g'' The Fay's identity states that with 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fay's trisecant identity」の詳細全文を読む スポンサード リンク
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