2003/04/30 by Ron Livné, Livné, Ron, Noriko Yui +1
Mathematics · #11F80 #11G40 #14G10 #14G32 #14J20 #14J27 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.AG #math.NT #msc:11F80 #msc:11G40 #msc:14G10 #msc:14G32 #msc:14J20 #msc:14J27 #msc:14J28
paper · pdf · doi:10.48550/arxiv.math/0304497
19 pages; some corrections made; see also related submission by Hulek-Verrill
openalex publication_date 2003/04/30 · arxiv created 2005/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a Calabi--Yau threefold fibred over \mathbb P1 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.