Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds, 1st Edition

  • Published By:
  • ISBN-10: 146146403X
  • ISBN-13: 9781461464037
  • DDC: 516.352
  • Grade Level Range: College Freshman - College Senior
  • 602 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on  Arithmetic and Geometry of  K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
List of Participants.
1: Introductory Lectures.
2: K3 and Enriques Surfaces.
3: Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi–Yau Varieties.
4: Two Lectures on the Arithmetic of K3 Surfaces.
5: Modularity of Calabi–Yau Varieties: 2011 and Beyond.
6: Research Articles: Arithmetic and Geometry of K3, Enriques and Other Surfaces.
7: Explicit Algebraic Coverings of a Pointed Torus.
8: Elliptic Fibrations on the Modular Surface Associated to Γ1 (8).
9: Universal Kummer Families Over Shimura Curves.
10: Numerical Trivial Automorphisms of Enriques Surfaces in Arbitrary Characteristic.
11: Picard-Fuchs Equations of Special One-Parameter Families of Invertible Polynomials.
12: A Structure Theorem for Fibrations on Delsarte Surfaces.
13: Fourier–Mukai Partners and Polarised K3 Surfaces.
14: On a Family of K3 Surfaces with I4 Symmetry.
15: Kind1 of Elliptically Fibered K3 Surfaces: A Tale of Two Cycles.
16: A Note About Special Cycles on Moduli Spaces of K3 Surfaces.
17: Enriques Surfaces of Hutchinson–Göpel Type and Mathieu Automorphisms.
18: Quartic K3 Surfaces and Cremona Transformations.
19: Invariants of Regular Models of the Product of Two Elliptic Curves at a Place of Multiplicative Reduction.
20: Research Articles: Arithmetic and Geometry of Calabi–Yau Threefolds and Higher Dimentional Varieties.
21: Dynamics of Special Points on Intermediate Jacobians.
22: Calabi–Yau Conifold Expansions.
23: Quadratic Twists of Rigid Calabi–Yau Threefolds Over ℚ.
24: Counting Sheaves on Calabi–Yau and Abelian Threefolds.
25: The Segre Cubic and Borcherds Products.
26: Quasi-modular Forms Attached to Hodge Structures.
27: The Zero Locus of the Infinitesimal Invariant.