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Morse cohomology estimates for jet differential operators

  • Jean-Pierre DemaillyEmail author
  • Mohammad Reza Rahmati
Article
  • 27 Downloads

Abstract

We provide detailed holomorphic Morse estimates for the cohomology of sheaves of jet differentials and their dual sheaves. These estimates apply on arbitrary directed varieties, and a special attention has been given to the analysis of the singular situation. As a consequence, we obtain existence results for global jet differentials and global differential operators under positivity conditions for the canonical or anticanonical sheaf of the directed structure.

Keywords

Directed variety Jet bundle Jet differential Jet metric Holomorphic Morse inequalities Canonical sheaf 

Mathematics Subject Classfication

32H30 32L10 14J17 14J40 53C55 

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Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Université de Grenoble-Alpes, Institut Fourier (Mathématiques), UMR 5582 du C.N.R.S.GièresFrance
  2. 2.Institute of Algebraic GeometryGottfried Wilhelm Leibniz Universität HannoverHannoverGermany

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