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J. Demailly - Existence of logarithmic and orbifold jet differentials

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Jean-Pierre Demailly
Fanny Bastien
Donovan Humphries
  • Fonction : Réalisateur

Résumé

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.

Dates et versions

medihal-02274631 , version 1 (30-08-2019)

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  • HAL Id : medihal-02274631 , version 1

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Jean-Pierre Demailly, Fanny Bastien, Donovan Humphries. J. Demailly - Existence of logarithmic and orbifold jet differentials: Summer School 2019 - Foliations and algebraic geometry. 2019. ⟨medihal-02274631⟩
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