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Lectures on K3 Surfaces

2016-09-26 Mathematics
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Release : 2016-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 252/5 ( reviews)

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Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts. This book was released on 2016-09-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Geometry

2017-02-16 Science
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Release : 2017-02-16
Genre : Science
Kind : eBook
Book Rating : 815/5 ( reviews)

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Book Synopsis Lectures on Geometry by : Edward Witten

Download or read book Lectures on Geometry written by Edward Witten. This book was released on 2017-02-16. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in an occasional series of volumes of CMI lectures. Although not explicitly linked, the topics in this inaugural volume have a common flavour and a common appeal to all who are interested in recent developments in geometry. They are intended to be accessible to all who work in this general area, regardless of their own particular research interests.

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

2013-06-12 Mathematics
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Release : 2013-06-12
Genre : Mathematics
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Book Rating : 03X/5 ( reviews)

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Book Synopsis Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by : Radu Laza

Download or read book Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds written by Radu Laza. This book was released on 2013-06-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

K3 Surfaces and Their Moduli

2016-04-22 Mathematics
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Release : 2016-04-22
Genre : Mathematics
Kind : eBook
Book Rating : 59X/5 ( reviews)

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Book Synopsis K3 Surfaces and Their Moduli by : Carel Faber

Download or read book K3 Surfaces and Their Moduli written by Carel Faber. This book was released on 2016-04-22. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds

2013-07-31
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Release : 2013-07-31
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Book Rating : 044/5 ( reviews)

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Book Synopsis Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds by : Radu Laza

Download or read book Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds written by Radu Laza. This book was released on 2013-07-31. Available in PDF, EPUB and Kindle. Book excerpt:

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