Cambridge University Press eBooks· 2016· Book chapter
Lectures on K3 Surfaces
- 403citations
- 2016year
Short summary
This book provides a comprehensive overview of K3 surfaces, a key class of Calabi-Yau manifolds in algebraic geometry, covering foundational concepts to recent breakthroughs like the Tate conjecture.
AI-generated from the title and abstract; the full text is not read.
Key points
- Examines K3 surfaces, a central class of Calabi-Yau manifolds in algebraic geometry.
- Covers foundational concepts and progresses to recent breakthroughs, including the Tate conjecture for K3 surfaces.
- Introduces techniques from arithmetic, homological, and differential geometry.
- Discusses key areas such as Hodge structures, moduli spaces, derived categories, and Chow rings.
AI-generated from the title and abstract; the full text is not read.
Abstract
K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2016 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Geometry and Topology
Geometry and TopologyMathematics