Pseudo-effective and nef cones on spherical varieties

Qifeng LI

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arXiv · 1311.6791

Pseudo-effective and nef cones on spherical varieties

Qifeng LI

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Abstract

We show that nef cycle classes on smooth complete spherical varieties are effective, and the products of nef cycle classes are also nef. Let X be a smooth projective spherical variety such that its effective cycle classes of codimension k are nef, where 1<= k <= dim(X)-1. We study the properties of X. And we show that if X is a toric variety, then X is isomorphic to the product of some projective spaces; if X is toroidal, then X is isomorphic to a rational homogeneous space; if X is horospherical, dim(X)>= 3 and k=2, then effective divisors on X are nef; if X is horospherical and effective divisors on X are nef, then there is a morphism from X to a rational homogeneous space such that each fiber is isomorphic to the product of some horospherical varieties of Picard number one.

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BibTeX RIS

Qifeng LI. 2013-11-26. Pseudo-effective and nef cones on spherical varieties. https://arxiv.org/abs/1311.6791

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