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prime form
In algebraic geometry, the Schottky–Klein prime form ''E''(''x'',''y'') of a compact Riemann surface ''X'' depends on two elements ''x'' and ''y'' of ''X'', and vanishes if and only if ''x'' = ''y''. The prime form ''E'' is not quite a holomorphic function on ''X'' × ''X'', but is a section of a holomorphic line bundle over this space. Prime forms were introduced by Friedrich Schottky and Felix Klein.
Prime forms can be used to construct meromorphic functions on ''X'' with given poles and zeros. If Σ''n''''i''''a''''i'' is a divisor linearly equivalent to 0, then Π''E''(''x'',''a''''i'')''n''''i'' is a meromorphic function with given poles and zeros.
==See also==
*Fay's trisecant identity
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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