Homogeneous projective bundles over abelian varieties

Abstract

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of commutative algebraic groups; the irreducible bundles correspond to Heisenberg groups and their standard representations. Our results extend those of Mukai on semi-homogeneous vector bundles, and yield a geometric view of the Brauer group of abelian varieties.

Final version, accepted for publication in Algebra and Number Theory Journal; 37 pages. This is a slightly shortened version of v3: Section 6 has been suppressed as well as the proofs of Propositions 4.1 and 4.2; Section 4 has been relegated to the very end

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