Effective and Big Divisors on a Projective Symmetric Variety

Details Effective and Big Divisors on a Projective Symmetric Variety Effective and Big Divisors on a Projective Symmetric Variety

2009-06-29

arxiv.org/abs/0906.5226v3

Mathematics

Algebraic Geometry

16 pages. We have added an explict description of the big cone as an union of cones whose closure is simplicial

Scientific paper

We describe the effective and the big cones of a projective symmetric variety. Moreover, we give a necessary and sufficient combinatorial criterion for the bigness of a nef divisor on a projective symmetric variety. When the variety is toroidal and the divisor is $G$-stable, such criterion has an explicit geometric interpretation. Finally, we describe the spherical closure of a symmetric subgroup.

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