Projective Contact Manifolds

Details Projective Contact Manifolds Projective Contact Manifolds

1998-10-16

arxiv.org/abs/math/9810102v2

Mathematics

Algebraic Geometry

LaTeX 2e, revised version

Scientific paper

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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