Verwandte Artikel zu Hyperbolicity of Projective Hypersurfaces (IMPA Monographs,...

Hyperbolicity of Projective Hypersurfaces (IMPA Monographs, 5, Band 5) - Hardcover

Diverio, Simone; Rousseau, Erwan

 
9783319323145: Hyperbolicity of Projective Hypersurfaces (IMPA Monographs, 5, Band 5)
Hardcover
ISBN 10: 3319323148 ISBN 13: 9783319323145
Verlag: Springer, 2016

Inhaltsangabe

This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these research fields (e.g. existence of Zariski dense entire curves should correspond to the (potential) density of rational points).

Perhaps one of the conjectures which generated most activity in Kobayashi hyperbolicity theory is the one formed by Kobayashi himself in 1970 which predicts that a very general projective hypersurface of degree large enough does not contain any (non-constant) entire curves. Since the seminal work of Green and Griffiths in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it became clear that a possible general strategy to attack this problem was to look at particular algebraic differential equations (jet differentials) that every entire curve must satisfy. This has led to some several spectacular results. Describing the state of the art around this conjecture is the main goal of this work.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

Simone Diverio is a 1st class CNRS researcher at the Institute of Mathematics of Jusseau - Paris Rive Gauche, France. He received his PhD (2008) jointly from the University of Grenoble I, France, and Sapienza University of Rome, Italy. In 2010 he was awarded the Prime d'Excellence Scientifique by the CNRS.
 
Erwan Rousseau is a professor at Aix-Marseille University, France. He did his PhD at Brest University, France (2004), with post-doc studies at the University of Quebéc, Canada and research at the University of Strasbourg (2010). In 2007, he was awarded the Cours Peccot du Collége de France.

Von der hinteren Coverseite

This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these research fields (e.g. existence of Zariski dense entire curves should correspond to the (potential) density of rational points).

Perhaps one of the conjectures which generated most activity in Kobayashi hyperbolicity theory is the one formed by Kobayashi himself in 1970 which predicts that a very general projective hypersurface of degree large enough does not contain any (non-constant) entire curves. Since the seminal work of Green and Griffiths in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it became clear that a possible general strategy to attack this problem was to look at particular algebraic differential equations (jet differentials) that every entire curve must satisfy. This has led to some several spectacular results. Describing the state of the art around this conjecture is the main goal of this work.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
3319323148
ISBN 13 
9783319323145
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
103
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Tiergartenstr. 17
Heidelberg
69121
Deutschland