Hyperbolicity of Projective Hypersurfaces

Erwan Rousseau

ISBN 10: 3319323148 / ISBN 13: 9783319323145

Published by Springer International Publishing, 2016

About this Item

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Bibliographic Details

• Title: Hyperbolicity of Projective Hypersurfaces
• Publisher: Springer International Publishing
• Publication Date: 2016
• Language: English
• ISBN 10: 3319323148
• ISBN 13: 9783319323145
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 12D millimeters 241 millimeters width by 160 millimeters height by 12 millimeters depth
• Weight: 330 grams

About this title

Synopsis

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.

About the Author

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.