Morse cohomology estimates for jet differential operators
Jean-Pierre Demailly (IF), Mohammad Reza Rahmati (IAG)
TL;DR
This paper develops Morse cohomology estimates for jet differential sheaves on directed varieties, enabling new existence results for global jet differentials and differential operators under positivity conditions.
Contribution
It provides detailed Morse estimates for jet differential sheaves on arbitrary directed varieties, including singular cases, advancing the understanding of their cohomology and existence results.
Findings
Morse estimates for jet differential sheaves on directed varieties
Existence of global jet differentials under positivity conditions
Analysis of singular situations in cohomology estimates
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 directedstructure.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology