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On the algebra of Siegel modular forms of genus $ 2$


Author: E. B. Vinberg
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 74 (2013), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2013, 1-13
MSC (2010): Primary 05A10, 11A07, 11C20, 11R04, 11S15
DOI: https://doi.org/10.1090/S0077-1554-2014-00217-X
Published electronically: April 9, 2014
MathSciNet review: 3235787
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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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Additional Information

E. B. Vinberg
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Moscow 119992, GSP–2, Russia

DOI: https://doi.org/10.1090/S0077-1554-2014-00217-X
Keywords: Symmetric domain, automorphic form, reflection group, moduli space, quartic surface, K3 surface, period map, categorical quotient
Published electronically: April 9, 2014
Article copyright: © Copyright 2014 American Mathematical Society