Geometry Over Nonclosed Fields | Buch

Cover: 9783319497624 | Geometry Over Nonclosed Fields | Fedor Bogomolov (u. a.) | Buch | ix

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Beschreibung

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 den Autor

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

Zusammenfassung

Covers exciting new research in the fields of classical algebraic geometry and arithmetic geometry

Examines recent research and results concerning K3-surfaces, including formulations of the Torelli Theorem for K3-surfaces and the arithmetic of K3-surfaces.

Provides students and researchers with fresh discussions of classical, long-standing problems.

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- "On the Kobayashi pseudometric, complex automorphisms and hyperahler manifolds" by Fedor Bogomolov, Ljudmila Kamenova, Steven Lu, and Misha Verbitsky.- "Lines on cubic hypersurfaces over finite fields" by Olivier Debarre, Antonio Laface, and Xavier Roulleau.- "Perverse sheaves of categories and non-rationality" by Andrew Harder, Ludmil Katzarkov, and Yijia Liu.- "Divisor classes and the virtual canonical bundle for genus zero maps" by A. J. de Jong and Jason Starr.- "A stronger derived Torelli theorem for K3 surfaces" by Max Lieblich and Martin Olsson.- "Morphisms to Brauer-Severi varieties, with applications to del Pezzo surfaces" by Christian Liedtke.- "Arithmetic of K3 surfaces" by Anthony Varilly-Alvarado.- "One-dimensional cohomology with finite coefficients and roots of unity" by Yuri G. Zarhin.

Details

Erscheinungsjahr:	2017
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	ix 261 S. 2 s/w Illustr. 1 farbige Illustr. 261 p. 3 illus. 1 illus. in color.
ISBN-13:	9783319497624
ISBN-10:	3319497626
Sprache:	Englisch
Herstellernummer:	978-3-319-49762-4
Einband:	Gebunden
Autor:	Bogomolov, Fedor Hassett, Brendan Tschinkel, Yuri
Redaktion:	Bogomolov, Fedor Tschinkel, Yuri Hassett, Brendan
Herausgeber:	Fedor Bogomolov/Brendan Hassett/Yuri Tschinkel
Auflage:	1st edition 2017
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 21 mm
Von/Mit:	Fedor Bogomolov (u. a.)
Erscheinungsdatum:	10.02.2017
Gewicht:	0,576 kg

Artikel-ID: 108486041