Overview
- Offers an updated, fresh view of hyperbolicity-type results about projective hypersurfaces
- Presents new and classical concepts, like the basics of Kobayashi hyperbolicity and algebraic hyperbolicity
- Is as self-contained as possible, and uses straightforward language
- Includes supplementary material: sn.pub/extras
Part of the book series: IMPA Monographs (IMPA, volume 5)
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Table of contents (6 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Hyperbolicity of Projective Hypersurfaces
Authors: Simone Diverio, Erwan Rousseau
Series Title: IMPA Monographs
DOI: https://doi.org/10.1007/978-3-319-32315-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2016
Hardcover ISBN: 978-3-319-32314-5Published: 21 July 2016
Softcover ISBN: 978-3-319-81253-3Published: 31 May 2018
eBook ISBN: 978-3-319-32315-2Published: 12 July 2016
Edition Number: 1
Number of Pages: XIV, 89
Number of Illustrations: 3 b/w illustrations
Topics: Differential Geometry, Algebraic Geometry, Several Complex Variables and Analytic Spaces