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Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Lecture Notes on Concentrated Graduate Courses

  • Book
  • © 2015

Overview

Editors:
  1. Radu Laza

    1. Mathematics Department, Stony Brook University, Stony Brook, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Matthias Schütt

    1. Leibniz Universität Hannover, Hannover, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Noriko Yui

    1. Department of Math & Stats, Queen's University, Kingston, Canada

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    You can also search for this editor in PubMed   Google Scholar

  • Fills a gap in the existing literature, presenting a friendly yet comprehensive introduction of the subject matter
  • Covers diverse streams of current research
  • Provides quick exposure to rapidly developing subjects

Part of the book series: Fields Institute Monographs (FIM, volume 34)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
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  2. K3 Surfaces: Arithmetic, Geometry and Moduli

    1. Front Matter

      Pages 1-1
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    2. The Geometry and Moduli of K3 Surfaces

      • Andrew Harder, Alan Thompson
      Pages 3-43

    3. Picard Ranks of K3 Surfaces of BHK Type

      • Tyler L. Kelly
      Pages 45-63

    4. Reflexive Polytopes and Lattice-Polarized K3 Surfaces

      • Ursula Whitcher
      Pages 65-79

  3. Hodge Theory and Transcendental Theory

    1. Front Matter

      Pages 81-81
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    2. An Introduction to Hodge Structures

      • Sara Angela Filippini, Helge Ruddat, Alan Thompson
      Pages 83-130

    3. Introduction to Nonabelian Hodge Theory

      • Alberto García-Raboso, Steven Rayan
      Pages 131-171

    4. Algebraic and Arithmetic Properties of Period Maps

      • Matt Kerr
      Pages 173-208

  4. Physics of Mirror Symmetry

    1. Front Matter

      Pages 209-209
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    2. Mirror Symmetry in Physics: The Basics

      • Callum Quigley
      Pages 211-278

  5. Enumerative Geometry: Gromov–Witten and Related Invariants

    1. Front Matter

      Pages 279-279
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    2. Introduction to Gromov–Witten Theory

      • Simon C. F. Rose
      Pages 281-301

    3. Introduction to Donaldson–Thomas and Stable Pair Invariants

      • Michel van Garrel
      Pages 303-313

    4. Donaldson–Thomas Invariants and Wall-Crossing Formulas

      • Yuecheng Zhu
      Pages 315-333

  6. Gross–Siebert Program

    1. Front Matter

      Pages 335-335
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    2. Enumerative Aspects of the Gross-Siebert Program

      • Michel van Garrel, D. Peter Overholser, Helge Ruddat
      Pages 337-420

  7. Modular Forms in String Theory

    1. Front Matter

      Pages 421-421
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    2. Introduction to Modular Forms

      • Simon C. F. Rose
      Pages 423-444

    3. Lectures on BCOV Holomorphic Anomaly Equations

      • Atsushi Kanazawa, Jie Zhou
      Pages 445-473
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Keywords

About this book

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.

Editors and Affiliations

  • Mathematics Department, Stony Brook University, Stony Brook, USA

    Radu Laza

  • Leibniz Universität Hannover, Hannover, Germany

    Matthias Schütt

  • Department of Math & Stats, Queen's University, Kingston, Canada

    Noriko Yui

Bibliographic Information

  • Book Title: Calabi-Yau Varieties: Arithmetic, Geometry and Physics

  • Book Subtitle: Lecture Notes on Concentrated Graduate Courses

  • Editors: Radu Laza, Matthias Schütt, Noriko Yui

  • Series Title: Fields Institute Monographs

  • DOI: https://doi.org/10.1007/978-1-4939-2830-9

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2015

  • Hardcover ISBN: 978-1-4939-2829-3Published: 30 August 2015

  • Softcover ISBN: 978-1-4939-4988-5Published: 22 October 2016

  • eBook ISBN: 978-1-4939-2830-9Published: 27 August 2015

  • Series ISSN: 1069-5273

  • Series E-ISSN: 2194-3079

  • Edition Number: 1

  • Number of Pages: X, 547

  • Number of Illustrations: 59 b/w illustrations, 12 illustrations in colour

  • Topics: Number Theory, Algebraic Geometry, Several Complex Variables and Analytic Spaces

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