Resumen de Geometry of rays-positive manifolds

Mauro C. Beltrametti, A. L. Knutsen, Antonio Lanteri, Carla Novelli

• Let be a smooth complex projective variety and let be a line bundle on it. Rays-positive manifolds, namely pairs (,) such that is numerically effective and ⋅?>0 for all extremal rays R on , 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 ?(,) is proven, describing as well the pairs with ?(,)=0,1 .