On the Frobenius Integrability of Certain Holomorphic p-Forms
By J. Demailly. 2000
73 citations recorded by the source corpus.
The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with semi-negative curvature on a compact Kahler manifold. There are in fact very strong restrictions, both on the holomorphic form and on the curvature of the semi-negative line bundle. In particular, these observations provide interesting information on the structure of projective manifolds which admit a contact structure: either they are Fano manifolds or, thanks to results of Kebekus-Peternell-Sommese-Wisniewski, they are biholomorphic to the projectivization of the cotangent bundle of another suitable projective manifold.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3d32b223e298320573c8c593169d6a904bc22a78
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Citations in the corpus
- Holomorphic symplectic geometry: a problem list (2010, unknown): “3) is proved in [13] by a case-by-case analysis (leading to a c mplete classification of those Poisson threefolds for which X0 = ∅).”
- A survey on the Campana-Peternell Conjecture (2014, background): “usly used in [33] to show that, with the exception of the manifolds of the form P(TZ), projective contact manifolds cannot have non constant Mori contractions. We may then conclude that: Theorem 5.7 ([14, 33]). Let Mbe a projective contact manifold. Then, either M is a Fano manifold of Picard number”
- Singular foliations with trivial canonical class (2011, background): “Demailly, in [24], proved that the identity of currents dωi = −∂φi ∧ ωi holds true, see also the proof of [14, Proposition 2.”