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- W2058441623 abstract "The starting point of this paper is the maximal extension Γ* t of Γ t , the subgroup of Sp 4 (ℚ) which is conjugate to the paramodular group. Correspondingly we call the quotient [Ascr ]* t =Γ* t ℍ 2 the minimal Siegel modular threefold. The space [Ascr ]* t and the intermediate spaces between [Ascr ] t =Γ t ℍ 2 which is the space of (1, t )-polarized abelian surfaces and [Ascr ]* t have not yet been studied in any detail. Using the Torelli theorem we first prove that [Ascr ]* t can be interpreted as the space of Kummer surfaces of (1, t )-polarized abelian surfaces and that a certain degree 2 quotient of [Ascr ] t which lies over [Ascr ]* t is a moduli space of lattice polarized K 3 surfaces. Using the action of Γ* t on the space of Jacobi forms we show that many spaces between [Ascr ] t and [Ascr ]* t possess a non-trivial 3-form, i.e. the Kodaira dimension of these spaces is non-negative. It seems a difficult problem to compute the Kodaira dimension of the spaces [Ascr ]* t themselves. As a first necessary step in this direction we determine the divisorial part of the ramification locus of the finite map [Ascr ] t →[Ascr ]* t . This is a union of Humbert surfaces which can be interpreted as Hilbert modular surfaces." @default.
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- W2058441623 date "1998-05-01" @default.
- W2058441623 modified "2023-10-10" @default.
- W2058441623 title "Minimal Siegel modular threefolds" @default.
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- W2058441623 doi "https://doi.org/10.1017/s0305004197002259" @default.
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