Geometry of rays-positive manifolds

Details Geometry of rays-positive manifolds Geometry of rays-positive manifolds

2011-08-03

arxiv.org/abs/1108.0897v1

Mathematics

Algebraic Geometry

18 pages; Collectanea Mathematica, published online 26 June 2011

Scientific paper

10.1007/s13348-011-0048-6

Let M be a smooth complex projective variety and let L be a line bundle on it. Rays-positive manifolds, namely pairs (M,L) such that L is numerically effective and L\cdotR > 0 for all extremal rays R on M, are studied. Several illustrative examples and some applications are provided. In particular, projective varieties with crepant singularities and of small degree with respect to the codimension are classified, and the non-negativity of the sectional genus g(M,L) is proven, describing as well the pairs with g(M,L) = 0,1.

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