Balanced line bundles and equivariant compactifications of homogeneous spaces
Algebraic Geometry
2013-07-23 v1
Abstract
Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety in terms of its global geometric invariants. The strongest form of the conjecture implies certain inequalities among geometric invariants of the variety and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanced line bundles, and prove the required inequalities for a large class of equivariant compactifications of homogeneous spaces.
Keywords
Cite
@article{arxiv.1307.5467,
title = {Balanced line bundles and equivariant compactifications of homogeneous spaces},
author = {Brendan Hassett and Sho Tanimoto and Yuri Tschinkel},
journal= {arXiv preprint arXiv:1307.5467},
year = {2013}
}
Comments
30 pages