Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses

✍ Scribed by Radu Laza, Matthias Schütt, Noriko Yui (eds.)

• Publisher: Springer-Verlag New York
• Year: 2015
• Tongue: English
• Leaves: 542
• Series: Fields Institute Monographs 34
• Edition: 1
• Category: Library

✦ Synopsis

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area.

The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-1
The Geometry and Moduli of K3 Surfaces....Pages 3-43
Picard Ranks of K3 Surfaces of BHK Type....Pages 45-63
Reflexive Polytopes and Lattice-Polarized K3 Surfaces....Pages 65-79
Front Matter....Pages 81-81
An Introduction to Hodge Structures....Pages 83-130
Introduction to Nonabelian Hodge Theory....Pages 131-171
Algebraic and Arithmetic Properties of Period Maps....Pages 173-208
Front Matter....Pages 209-209
Mirror Symmetry in Physics: The Basics....Pages 211-278
Front Matter....Pages 279-279
Introduction to Gromov–Witten Theory....Pages 281-301
Introduction to Donaldson–Thomas and Stable Pair Invariants....Pages 303-313
Donaldson–Thomas Invariants and Wall-Crossing Formulas....Pages 315-333
Front Matter....Pages 335-335
Enumerative Aspects of the Gross-Siebert Program....Pages 337-420
Front Matter....Pages 421-421
Introduction to Modular Forms....Pages 423-444
Lectures on BCOV Holomorphic Anomaly Equations....Pages 445-473
Polynomial Structure of Topological String Partition Functions....Pages 475-500
Front Matter....Pages 501-501
Introduction to Arithmetic Mirror Symmetry....Pages 503-539
Back Matter....Pages 541-547

✦ Subjects

Number Theory; Algebraic Geometry; Several Complex Variables and Analytic Spaces