Journal of Mathematics of Kyoto University

On the image of code polynomials under theta map

Manabu Oura and Riccardo Salvati Manni

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The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for $g\leq 3$ and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for $g\geq 5$. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for $g\geq 4$ and consequently we get the non surjectivity of the graded rings for the remaining case $g=4$.

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J. Math. Kyoto Univ., Volume 48, Number 4 (2008), 895-906.

First available in Project Euclid: 14 August 2009

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Oura, Manabu; Salvati Manni, Riccardo. On the image of code polynomials under theta map. J. Math. Kyoto Univ. 48 (2008), no. 4, 895--906. doi:10.1215/kjm/1250271322.

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