On the image of code polynomials under theta map

Details On the image of code polynomials under theta map On the image of code polynomials under theta map

2008-03-31

arxiv.org/abs/0803.4389v1

Mathematics

Number Theory

Scientific paper

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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