Hyperbolicity of Projective Hypersurfaces
Autores
Descrição
Oferece uma visão moderna e atualizada de resultados de hiperbolicidade sobre hipersuperfícies projetivas.
Apresenta conceitos novos e clássicos, como o básico da hiperbolicidade de Kobayashi e hiperbolicidade algébrica.
É o mais auto-suficiente possível e usa linguagem diret
Comprar
Nome: Hyperbolicity of Projective Hypersurfaces
Autor(es): Erwan Rousseau e Simone Diverio
Páginas: 87
Publicação: IMPA-Springer 2016
ISBN: 978-3-319-32314-5
Edição: 1
1 Kobayashi Hyperbolicity: basic theory
1.1 The Kobayashi distance
1.2 Brody’s criteion for hyperbolicity
1.3 Riemann surfaces and uniformization
2 Algebraic hyperbolicity
2.1 Hyperbolicity and genus of curves
2.2 Algebraic hyperbolicity of generic projective hypersurfaces of high degree
2.3 A brief history of the above results
3 Jets spaces
3.1 Projectivization of directed manifolds
3.2 Projectivized jet bundles
3.3 Jet differentials
4 Hyperbolicity and negativity of the curvature
4.1 Curvature and positivity
4.2 The Ahlfors-Schwarz lemma
4.3 A general strategy for algebraic degeneracy
5 Hyperbolicity of generic surfaces in projective 3-space
5.1 General strategy
5.2 Existence of jet differentials
5.3 Global generation of the twisted tangent space of the universal family
5.4 Proof of the hyperbolicity
6 Algebraic degeneracy for generic projective hypersurfaces
6.1 Statement of the result and scheme of the proof
6.2 Existence of the jet differentials
6.3 Proof of the existence of jet differentials in dimension 3
6.4 Proof of the existence of jet differentials in higher dimensions
6.5 Meromorphic vector fields
6.6 Effective aspects
Bibliography