## Figures from this paper

## 41 Citations

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We show that a pseudoeffective R-divisor has numerical dimension 0 if it is numerically trivial on a subvariety with ample normal bundle. This implies that the cycle class of a curve with ample…

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We establish a Grothendieck--Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more generally, for smooth…

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Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration…

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Abstract In this note we study properties of partially ample line bundles on simplicial projective toric varieties. We prove that the cone of q-ample line bundles is a union of rational polyhedral…

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The goal of this article is twofold. On one hand, we study the subvarieties of projective varieties which possess partially ample normal bundle; we prove that they are G2 in the ambient space. This…

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The goal of this article is to define partially ample subvarieties of projective varieties, generalizing Ottem’s work on ample subvarieties, and also to show their ubiquity. As an application, we…

### Positive cones of dual cycle classes

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We study generalizations for higher codimension cycles of several well-known definitions of the nef cone of divisors on a projective variety. These generalizations fix some of the pathologies…

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Partially ample divisors are defined by relaxing the different conditions that characterize the ample divisors. We prove that for nef and big divisors such notions coincide. We also prove that the…

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We determine an upper bound for the cohomological dimension of the complement of a closed subset in a projective variety which possesses an appropriate stratification. We apply the result to several…

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We generalize some results of A.J. Sommese, B. Totaro and M.V. Brown, providing some geometric interpretations of the notion of partial ampleness.

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