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Projective varieties and rings of Thetanullwerte

Published online by Cambridge University Press:  22 January 2016

Riccardo Salvati Manni
Riccardo Salvati Manni*
Affiliation:
Dipartimento di Matematica, Università «La Sapienza», 00185 Roma, Italy
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Let r denote an even positive integer, m an element of Q2g such that r·m ≡ 0 mod 1 and ϑm the holomorphic function on the Siegel upper-half space Hg defined by

(1) ,

in which e(t) stands for exp and m′ and m″ are the first and the second entry vector of m. Let Θg(r) denote the graded ring generated over C by such Thetanullwerte; then it is a well known fact that the integral closure of Θg(r) is the ring of all modular forms relative to Igusa’s congruence subgroup Γg(r2, 2r2) cf. [6]. We shall denote this ring by A(Γg(r2, 2r2)).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 165 - 176
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

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