Balanced line bundles and equivariant compactifications of homogeneous spaces

By Brendan Hassett, Sho Tanimoto, Yuri Tschinkel. 2013

54 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe9d22d48119208da9b9e666fbb2694d8689be6f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Sho Tanimoto
2. Brian Lehmann
3. Akash Kumar Sengupta
4. Nguyen-Bac Dang

In Mathematical Physics

1. Brian Lehmann
2. Akash Kumar Sengupta
3. Sho Tanimoto

Citations in the corpus

• Geometric consistency of Manin's conjecture (2018, result): “This theorem generalizes earlier partial results in [BT98b], [HTT15], [LTT16], [HJ17], [LT17b], and [Sen17].”