English

Geometry of rays-positive manifolds

Algebraic Geometry 2011-08-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1108.0897,
  title  = {Geometry of rays-positive manifolds},
  author = {Mauro C. Beltrametti and Andreas Leopold Knutsen and Antonio Lanteri and Carla Novelli},
  journal= {arXiv preprint arXiv:1108.0897},
  year   = {2011}
}

Comments

18 pages; Collectanea Mathematica, published online 26 June 2011

R2 v1 2026-06-21T18:46:05.800Z