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.
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