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Erschienen in:
K3 and Enriques Surfaces Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

Modularity of Calabi–Yau Varieties: 2011 and Beyond

verfasst von : Noriko Yui

Erschienen in: Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Verlag: Springer New York

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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 \(\mathbb{Q}\) 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. The topic (4) is commonly known as geometric modularity.
Discussions in this paper are centered around arithmetic modularity, namely on (1), and (2), with a brief excursion to (3).

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Vorheriges Kapitel Two Lectures on the Arithmetic of K3 Surfaces
Nächstes Kapitel Explicit Algebraic Coverings of a Pointed Torus
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Metadaten
Titel
Modularity of Calabi–Yau Varieties: 2011 and Beyond
verfasst von
Noriko Yui
Copyright-Jahr
2013
Verlag
Springer New York
Buch
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Print ISBN: 978-1-4614-6402-0

Electronic ISBN: 978-1-4614-6403-7

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-6403-7_4