Projective Contact Manifolds
Abstract
We prove that a projective contact manifold X with second Betti number at least 2 whose canonical bundle KX is not nef, is always the projectivised tangent bundle P(TY) 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 KX2 = 0 and KX 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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