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- Date de réalisation : 1 Juillet 2019
- Durée du programme : 66 min
- Classification Dewey : Mathématiques
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- Catégorie : Conférences
- Niveau : niveau Doctorat (LMD), Recherche
- Disciplines : Mathématiques
- Collections : Ecoles d'été, 2019
- ficheLom : Voir la fiche LOM
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- Auteur(s) : Demailly Jean-Pierre
- Réalisateur(s) : Bastien Fanny, HUMPHRIES Donovan
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- Langue : Anglais
- Mots-clés : Grenoble, eem2019, Foliations and algebraic geometry, Feuilletages et géométrie algébrique, logarithmic jet differentials, orbifold jet differentials
- Conditions d’utilisation / Copyright : CC BY-NC-ND 4.0
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J. Demailly - Existence of logarithmic and orbifold jet differentials
Given
a projective algebraic orbifold, one can define associated logarithmic
and orbifold jet bundles. These bundles describe the algebraic
differential operators that act on germs of curves satisfying ad hoc
ramification conditions. Holomorphic Morse inequalities can be used to
derive precise cohomology estimates and, in particular, lower bounds for
the dimensions of spaces of global jet differentials. A striking
consequence is that, under suitable geometric hypotheses, the
corresponding entire curves must satisfy nontrivial algebraic
differential equations. These results extend those obtained by the
author in 2010, and are based on recent joint work with F. Campana, L.
Darondeau and E. Rousseau.
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