The modularity of the Barth-Nieto quintic and its relatives
| dc.creator | Hulek, K. | |
| dc.creator | Spandaw, J. | |
| dc.creator | van Geemen, B. | |
| dc.creator | van Straten, D. | |
| dc.date | 2000-10-05 | |
| dc.date.accessioned | 2026-07-07T04:37:51Z | |
| dc.date.available | 2026-07-07T04:37:51Z | |
| dc.description | The moduli space of (1,3)-polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth-Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y, respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L-function of their common third étale cohomology group is modular, as predicted by a conjecture of Fontaine and Mazur. The corresponding modular form is the unique normalized cusp form of weight 4 for the group Γ_1(6). By Tate's conjecture, this should imply that Y, the fibred square of the universal elliptic curve S_1(6), and Verrill's rigid Calabi-Yau Z_{A_3}, which all have the same L-function, are in correspondence over Q. We show that this is indeed the case by giving explicit maps. | |
| dc.description | 30 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0010049 | |
| dc.identifier | http://arxiv.org/abs/math/0010049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60059 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | The modularity of the Barth-Nieto quintic and its relatives | |
| dc.type | text |