On the algebra of Siegel modular forms of genus 2

Vinberg, E.

doi:10.1090/S0077-1554-2014-00217-X

On the algebra of Siegel modular forms of genus $2$
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by E. B. Vinberg

Trans. Moscow Math. Soc. 2013, 1-13

DOI: https://doi.org/10.1090/S0077-1554-2014-00217-X

Published electronically: April 9, 2014

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Abstract:

Using the methods of our 2010 paper, we recover the old result of J. Igusa, saying that the algebra of even Siegel modular forms of genus $2$ is freely generated by forms of weights $4,6,10,12$. We also determine the structure of the algebra of all Siegel modular forms of genus $2$ and, in particular, interpret the supplementary generator of odd weight as the Jacobian of the generators of even weights.

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