Hyperbolicity of Projective Hypersurfaces

Simone Diverio, Erwan Rousseau (Autoren)

Buch | Softcover

XIV, 89 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-81253-3 (ISBN)

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lt;p>Thisbook presents recent advances on Kobayashi hyperbolicity in complex geometry,especially in connection with projective hypersurfaces. This is a very activefield, not least because of the fascinating relations with complex algebraicand arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta,among others, resulted in precise conjectures regarding the interplay of theseresearch fields (e.g. existence of Zariski dense entire curves shouldcorrespond to the (potential) density of rational points).

Perhapsone of the conjectures which generated most activity in Kobayashi hyperbolicitytheory is the one formed by Kobayashi himself in 1970 which predicts that avery general projective hypersurface of degree large enough does not containany (non-constant) entire curves. Since the seminal work of Green and Griffithsin 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, itbecame clear that a possible general strategy to attack this problem was tolook at particular algebraic differential equations (jet differentials) thatevery entire curve must satisfy. This has led to some several spectacularresults. Describing the state of the art around this conjecture is the maingoal of this work.

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.

- Introduction.- Kobayashi hyperbolicity: basic theory.- Algebraic hyperbolicity.- Jets spaces.- Hyperbolicity and negativity of the curvature.- Hyperbolicity of generic surfaces in projective 3-space.- Algebraic degeneracy for projective hypersurfaces.

Erscheint lt. Verlag	31.5.2018
Reihe/Serie	IMPA Monographs
Zusatzinfo	XIV, 89 p. 3 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1708 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	14F10 • 14J70 • 32Q45 • entire curves • hypersurfaces • jet differentials • jet spaces • Kobayashi Hyperbolicity
ISBN-10	3-319-81253-X / 331981253X
ISBN-13	978-3-319-81253-3 / 9783319812533
Zustand	Neuware