Hardcover. 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

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Bibliographic Details

Title: Geometry Over Nonclosed Fields (Hardcover)
Publisher: Springer International Publishing AG, Cham
Publication Date: 2017
Language: English
ISBN 10: 3319497626
ISBN 13: 9783319497624
Binding: Hardcover
Edition: 1st Edition
Condition: new

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

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