Geometry Over Nonclosed Fields

Fedor Bogomolov

ISBN 10: 3319842358 / ISBN 13: 9783319842356

Verlag: Springer International Publishing, Springer International Publishing Jul 2018, 2018

Beschreibung

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 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 272 pp. Englisch.

Bestandsnummer des Verkäufers 9783319842356

Bibliografische Details

• Titel: Geometry Over Nonclosed Fields
• Verlag: Springer International Publishing, Springer International Publishing Jul 2018
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 3319842358
• ISBN-13: 9783319842356
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 15 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 15 mm
• Gewicht: 417 Gramm

Über diesen Titel

Inhaltsangabe

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. 

Über die Autorin bzw. den Autor

Fedor Bogomolov, Courant Institute of Mathematical Sciences, New York, NYBrendan Hassett, Brown University, Providence, Rhode IslandYuri Tshinkel,Courant Institute of Mathematical Sciences, New York, NY