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Geometry over nonclosed fields

Bogomolov, Fedor.

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Geometry over nonclosed fields

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry over nonclosed fields/ edited by Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel.
other author:	Bogomolov, Fedor.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	ix, 261 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Geometry, Algebraic. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-49763-1
ISBN:	9783319497631

Geometry over nonclosed fields
Geometry over nonclosed fields[electronic resource] /edited by Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel. - Cham :Springer International Publishing :2017. - ix, 261 p. :ill., digital ;24 cm. - Simons symposia,2365-9564. - Simons symposia..

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.

ISBN: 9783319497631

Standard No.: 10.1007/978-3-319-49763-1doiSubjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Geometry over nonclosed fields
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490 1 $a Simons symposia, $x 2365-9564
520 $a 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.
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