Author(s): Diverio, S. (ed.) Claudon, Benoît; Corvaja, Pietro; Demailly, Jean-Pierre; Diverio, Simone; Duval, Julien; Gasbarri, Carlo; Kebekus, Stefan; Paun, Mihai; Rousseau, Erwan; Sibony, Nessim; Taji, Behrouz; Voisin, Claire
Series: Panoramas et Synthèses 56
Publisher: Société Mathématique de France
Year: 2021
Language: English
Pages: 353
0pt20ptRésumés des articles
0pt20ptAbstracts
0pt20ptINTRODUCTION
0pt20ptACKNOWLEDGMENTS
title
1. Brody lemma
2. A variant
References
title
1. Introduction
2. Preliminaries
3. Basics of Nevanlinna Theory for Parabolic Riemann Surfaces
4. The Vanishing Theorem
5. Bloch Theorem
6. Parabolic Curves Tangent to Holomorphic Foliations
7. Brunella index theorem
References
title
1. Introduction
2. The approach via foliations
3. Orbifold Bogomolov-Miyaoka-Yau inequalities
4. Applications
References
title
0. Introduction
1. Hyperbolicity concepts
2. Semple tower associated to a directed manifold
3. Jet differentials and Green-Griffiths bundles
4. Existence of hyperbolic hypersurfaces of low degree
5. Proof of the Kobayashi conjecture on the hyperbolicity of general hypersurfaces
References
title
1. Introduction
2. Curves of bounded genus on surfaces with big cotangent bundle
3. Entire curves on surfaces with big cotangent bundle
4. An approach to the general case of Green-Griffiths conjecture for surfaces
References
title
1. Introduction
2. Definitions and Notation
Part I. Fractional semipositivity and application to hyperbolicity
3. Logarithmic differentials with fractional pole order
4. Fractional tangents and foliations
5. Fractional semipositivity
6. Application to hyperbolicity
Part II. Proof of the semipositivity result
7. Positivity of relative dualising sheaves
8. Failure of semipositivity, construction of morphisms
9. Proof of the semipositivity result
References
title
1. Introduction
2. Complex differential geometric background and hyperbolicity
3. Motivations from birational geometry
4. An example by J.-P. Demailly
5. The Wu-Yau theorem
6. The Kähler case, and the quasi-negative holomorphic sectional curvature case
References
title
1. Introduction
2. Heights, Diophantine approximation
3. Higher dimensional Diophantine approximation
4. A proof of Siegel's theorem for integral points on curves
5. The generalized Fermat equation and triangle groups
6. Algebraic groups and the S-unit equation theorem
7. Integral points on surfaces
References
title
0. Introduction
1. Fibrations and holomorphic forms
2. Fibrations from families of cycles
3. MRC and -fibrations
4. Special varieties and the core
References
