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Trudy Moskovskogo Matematicheskogo Obshchestva, 2013, Volume 74, Issue 1, Pages 1–16 (Mi mmo538)  
This article is cited in 17 scientific papers (total in 17 papers)

On the algebra of Siegel modular forms of genus 2

È. B. Vinberg

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (301 kB) Citations (17)
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Abstract: Using the methods of the author [Transform. Groups 15, No. 3, 701–741 (2010; Zbl 1225.05015)], we recover the old result of J. Igusa [Am. J. Math. 86, 392–412 (1964; Zbl 0133.33301)], 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.
Key words and phrases: symmetric domain; automorphic form; reflection group; moduli space; quartic surface; K3 surface; period map; categorical quotient.
Received: 04.01.2013
Revised: 04.02.2013
English version:
Transactions of the Moscow Mathematical Society, 2013, Volume 74, Pages 1–13
DOI: https://doi.org/10.1090/S0077-1554-2014-00217-X
Bibliographic databases:
Document Type: Article
UDC: 515.178.1.
MSC: 1F46
Language: Russian
Citation: È. B. Vinberg, “On the algebra of Siegel modular forms of genus 2”, Tr. Mosk. Mat. Obs., 74, no. 1, MCCME, M., 2013, 1–16; Trans. Moscow Math. Soc., 74 (2013), 1–13
Citation in format AMSBIB
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\paper On the algebra of Siegel modular forms of genus~2
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\transl
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