TY - JOUR

T1 - The modularity of certain non-rigid Calabi-Yau threefolds

AU - Livné, Ron

AU - Yui, Noriko

PY - 2005

Y1 - 2005

N2 - Let X be a Calabi-Yau threefold fibred over ℙ1 by non-constant semi-stable K3 surfaces and reaching the Arakelov-Yau bound. In [25], 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 [17] and [28] 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.

AB - Let X be a Calabi-Yau threefold fibred over ℙ1 by non-constant semi-stable K3 surfaces and reaching the Arakelov-Yau bound. In [25], 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 [17] and [28] 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.

UR - http://www.scopus.com/inward/record.url?scp=33744725218&partnerID=8YFLogxK

U2 - 10.1215/kjm/1250281650

DO - 10.1215/kjm/1250281650

M3 - Article

AN - SCOPUS:33744725218

SN - 0023-608X

VL - 45

SP - 645

EP - 665

JO - Kyoto Journal of Mathematics

JF - Kyoto Journal of Mathematics

IS - 4

ER -