Modularity of Calabi--Yau varieties: 2011 and beyond
Abstract
This paper presents the current status on modularity of Calabi-Yau varieties since the last update in 2003. We will focus on Calabi-Yau varieties of dimension at most three. Here modularity refers to at least two different types: arithmetic modularity and geometric modularity. These will include: (1) the modularity (automorphy) of Galois representations of Calabi-Yau varieties (or motives) defined over Q or number fields, (2) the modularity of solutions of Picard--Fuchs differential equations of families of Calabi-Yau varieties, and mirror maps (mirror moonshine), (3) the modularity of generating functions of invariants counting certain quantities on Calabi-Yau varieties, and (4) the modularity of moduli for families of Calabi-Yau varieties.
Keywords
Cite
@article{arxiv.1212.4308,
title = {Modularity of Calabi--Yau varieties: 2011 and beyond},
author = {Noriko Yui},
journal= {arXiv preprint arXiv:1212.4308},
year = {2012}
}
Comments
33 pages