Minimal Siegel modular threefolds
| dc.creator | Gritsenko, Valeri | |
| dc.creator | Hulek, Klaus | |
| dc.date | 1995-06-23 | |
| dc.date | 1996-01-10 | |
| dc.date.accessioned | 2026-07-07T08:57:58Z | |
| dc.date.available | 2026-07-07T08:57:58Z | |
| dc.description | In this paper we study the maximal extension $Γ_t^*$ of the subgroup $Γ_t$ of $\operatorname{Sp}_4 (\bq)$ which is conjugate to the paramodular group. The index of this extension is $2^{ν(t)}$ where $ν(t)$ is the number of prime divisors of $t$. The group $Γ_t^*$ defines the minimal modular threefold ${\Cal A}_t^*$ which is a finite quotient of the moduli space ${\Cal A}_t$ of $(1,t)$-polarized abelian surfaces. A certain degree 2 quotient of ${\Cal A}_t$ is a moduli space of lattice polarized $K3$ surfaces. The space ${\Cal A}_t^*$ can be interpreted as the space of Kummer surfaces associated to $(1,t)$-polarized abelian surfaces. Using the action of $Γ_t^*$ on the space of Jacobi forms we show that many spaces between ${\Cal A}_t$ and ${\Cal A}_t^*$ posess a non-trivial 3-form, i.e. the Kodaira dimension of these spaces is non-negative. Finally we determine the divisorial part of the ramification locus of the finite map ${\Cal A}_t\rightarrow {\Cal A}_t^*$ which is a union of Humbert surfaces. We interprete the corresponding Humbert surfaces as Hilbert modular surfaces. | |
| dc.description | We have included a theorem explaining the connection of the minimal Siegel modular threefold with the space of Kummer surfaces of abelian surfaces with non-principal polarization. AMSTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9506017 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9506017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147143 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Minimal Siegel modular threefolds | |
| dc.type | text |