The Modular Form of the Barth-Nieto Quintic
| dc.creator | Gritsenko, V. | |
| dc.creator | Hulek, K. | |
| dc.date | 1998-06-03 | |
| dc.date.accessioned | 2026-07-07T05:24:55Z | |
| dc.date.available | 2026-07-07T05:24:55Z | |
| dc.description | Barth and Nieto have found a remarkable quintic threefold which parametrizes Heisenberg invariant Kummer surfaces which belong to abelian surfaces with a (1,3)-polarization and a lecel 2 structure. A double cover of this quintic, which is also a Calabi-Yau variety, is birationally equivalent to the moduli space {\cal A}_3(2) of abelian surfaces with a (1,3)-polarization and a level 2 structure. As a consequence the corresponding paramodular group Γ_3(2) has a unique cusp form of weight 3. In this paper we find this cusp form which is Δ_1^3. The form Δ_1 is a remarkable weight 1 cusp form with a character with respect to the paramodular group Γ_3. It has several interesting properties. One is that it admits an infinite product representation, the other is that it vanishes of order 1 along the diagonal in Siegel space. In fact Δ_1 is an element of a short series of modular forms with this last property. Using the fact that Δ_1 is a weight 3 cusp form with respect to the group Γ_3(2) we give an independent construction of a smooth projective Calabi-Yau model of the moduli space {\cal A}_3(2). | |
| dc.description | 20 pages, Latex2e RIMS Preprint 1203 | |
| dc.identifier | https://arxiv.org/abs/math/9806011 | |
| dc.identifier | http://arxiv.org/abs/math/9806011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76991 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The Modular Form of the Barth-Nieto Quintic | |
| dc.type | text |