Journal of Mathematics of Kyoto University

On the image of code polynomials under theta map

Abstract

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 $g=4$.

Article information

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

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250271322

Digital Object Identifier
doi:10.1215/kjm/1250271322

Mathematical Reviews number (MathSciNet)
MR2513590

Zentralblatt MATH identifier
1247.11074

Citation

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. https://projecteuclid.org/euclid.kjm/1250271322