Differential equations as embedding obstructions and vanishing theorems
Damian Brotbek (IRMAR)
TL;DR
This paper extends vanishing theorems for cohomology of symmetric powers of cotangent bundles and applies these to derive new results on jet differential bundles, advancing understanding in algebraic geometry.
Contribution
It generalizes a vanishing theorem for symmetric powers of cotangent bundles and introduces new vanishing results for Green-Griffiths jet bundles.
Findings
New vanishing theorems for cohomology of symmetric powers
Extended vanishing results for jet differential bundles
Generalizations of prior results by Diverio and Pacienza-Rousseau
Abstract
We generalize a vanishing theorem for the cohomology of symmetric powers of the cotangent bundle of subvarieties of projective space due to Schneider. From this we deduce new vanishing results for Green-Griffiths jet differential bundles, generalizing results of Diverio and Pacienza-Rousseau.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons