Morse cohomology estimates for jet differential operators

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 re...

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Bibliographic Details
Published in:Bollettino della Unione matematica italiana (2008) 2019-03, Vol.12 (1-2), p.145-164
Main Authors: Demailly, Jean-Pierre, Rahmati, Mohammad Reza
Format: Article
Language:English
Subjects:
Differential equations
Estimates
Homology
Mathematics
Mathematics and Statistics
Operators (mathematics)
Sheaves
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Summary: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.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-018-0172-2