Ebook: Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

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.

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both the 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 large 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 three days of introductory lectures. A selection of four of these lectures is included in this volume. These lectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject.

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both the 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 large 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 three days of introductory lectures. A selection of four of these lectures is included in this volume. These lectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject.

Content:
Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
K3 and Enriques Surfaces....Pages 3-28
Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi–Yau Varieties....Pages 29-69
Two Lectures on the Arithmetic of K3 Surfaces....Pages 71-99
Modularity of Calabi–Yau Varieties: 2011 and Beyond....Pages 101-139
Front Matter....Pages 141-141
Explicit Algebraic Coverings of a Pointed Torus....Pages 143-152
Universal Kummer Families Over Shimura Curves....Pages 153-199
Numerical Trivial Automorphisms of Enriques Surfaces in Arbitrary Characteristic....Pages 201-265
Picard–Fuchs Equations of Special One-Parameter Families of Invertible Polynomials....Pages 267-283
A Structure Theorem for Fibrations on Delsarte Surfaces....Pages 285-310
A Note About Special Cycles on Moduli Spaces of K3 Surfaces....Pages 311-332
Enriques Surfaces of Hutchinson–G?pel Type and Mathieu Automorphisms....Pages 333-365
Quartic K3 Surfaces and Cremona Transformations....Pages 367-386
Invariants of Regular Models of the Product of Two Elliptic Curves at a Place of Multiplicative Reduction....Pages 387-409
Front Matter....Pages 411-427
Dynamics of Special Points on Intermediate Jacobians....Pages 429-454
Calabi–Yau Conifold Expansions....Pages 455-460
Front Matter....Pages 461-487
Counting Sheaves on Calabi–Yau and Abelian Threefolds....Pages 489-489
The Segre Cubic and Borcherds Products....Pages 491-498
Quasi-modular Forms Attached to Hodge Structures....Pages 499-515
The Zero Locus of the Infinitesimal Invariant....Pages 517-533
....Pages 489-489