Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces

Brendan Hassett, Sho Tanimoto, Yuri Tschinkel

Research output: Contribution to journalArticlepeer-review

Abstract

Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X 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.

Original languageEnglish (US)
Pages (from-to)6375-6410
Number of pages36
JournalInternational Mathematics Research Notices
Volume2015
Issue number15
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)

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