Modularity of Calabi--Yau varieties: 2011 and beyond

Autor:	Yui, Noriko
Rok vydání:	2012
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11G42 11F80 11G40 14J15 14J32 14J33
Druh dokumentu:	Working Paper
Popis:	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. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1212.4308 Zobrazit plný text záznamu View this record from Arxiv