Geometry Over Nonclosed Fields

Fedor Bogomolov

ISBN 10: 3319842358 / ISBN 13: 9783319842356

Published by Springer International Publishing Jul 2018, 2018

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations.One main recent insight the book covers is theidea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail. 272 pp. Englisch.

Seller Inventory # 9783319842356

Bibliographic Details

• Title: Geometry Over Nonclosed Fields
• Publisher: Springer International Publishing Jul 2018
• Publication Date: 2018
• Language: English
• ISBN 10: 3319842358
• ISBN 13: 9783319842356
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 15D millimeters 235 millimeters width by 155 millimeters height by 15 millimeters depth
• Weight: 417 grams

About this title

Synopsis

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail. 

About the Author

Fedor Bogomolov, Courant Institute of Mathematical Sciences, New York, NY

Brendan Hassett, Brown University, Providence, Rhode Island

Yuri Tshinkel,Courant Institute of Mathematical Sciences, New York, NY