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Projective Contact Manifolds

Stefan Kebekus·Thomas Peternell·Andrew J. Sommese·Jaroslaw Wisniewski
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Abstract

We prove that a projective contact manifold X with second Betti number at least 2 whose canonical bundle K_X is not nef, is always the projectivised tangent bundle P(T_Y) of a projective manifold Y. It is expected that the canonical bundle of a projective contact manifold is never nef; we prove this unless possibly K_X^2 = 0 and K_X is not numerically trivial. Moreover we study more generally nef subsheaves of rank 1 in the cotangent bundle which are proportional to the canonical bundle.

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Stefan Kebekus, Thomas Peternell, Andrew J. Sommese, Jaroslaw Wisniewski. 1999-09-27. Projective Contact Manifolds. https://arxiv.org/abs/math/9810102

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