Geometry of rays-positive manifolds

M. C. Beltrametti1, A. L. Knutsen2, A. Lanteri3, C. Novelli4
1Dipartimento di Matematica, Università di Genova, Genoa, Italy
2Department of Mathematics, University of Bergen, Bergen, Norway
3Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, Milano, Italy
4Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Padova, Italy

Tóm tắt

Let $${\mathcal {M}}$$ be a smooth complex projective variety and let $${\mathcal {L}}$$ be a line bundle on it. Rays-positive manifolds, namely pairs $${(\mathcal {M},\mathcal {L})}$$ such that $${\mathcal {L}}$$ is numerically effective and $${\mathcal {L}\cdot R >0 }$$ for all extremal rays R on $${\mathcal {M}}$$ , 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 $${g(\mathcal {M},\mathcal {L})}$$ is proven, describing as well the pairs with $${g(\mathcal {M},\mathcal {L})=0,1}$$ .

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