The modularity of certain non-rigid Calabi-Yau threefolds
| dc.creator | Livné, Ron | |
| dc.creator | Yui, Noriko | |
| dc.date | 2003-04-30 | |
| dc.date | 2005-06-18 | |
| dc.date.accessioned | 2026-07-07T04:57:37Z | |
| dc.date.available | 2026-07-07T04:57:37Z | |
| dc.description | Let $X$ be a Calabi--Yau threefold fibred over ${\mathbb P}^1$ by non-constant semi-stable K3 surfaces and reaching the Arakelov--Yau bound. In [STZ], X. Sun, Sh.-L. Tan, and K. Zuo proved that $X$ is modular in a certain sense. In particular, the base curve is a modular curve. In their result they distinguish the rigid and the non-rigid cases. In [SY] and [V] rigid examples were constructed. In this paper we construct explicit examples in non-rigid cases. Moreover, we prove for our threefolds that the ``interesting'' part of their $L$-series is attached to an automorphic form, and hence that they are modular in yet another sense. | |
| dc.description | 19 pages; some corrections made; see also related submission by Hulek-Verrill | |
| dc.identifier | https://arxiv.org/abs/math/0304497 | |
| dc.identifier | http://arxiv.org/abs/math/0304497 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67321 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G32, 14J28, 14J27, 14J20, 14G10, 11G40, 11F80 | |
| dc.title | The modularity of certain non-rigid Calabi-Yau threefolds | |
| dc.type | text |