Homogeneous projective bundles over abelian varieties

Details Homogeneous projective bundles over abelian varieties Homogeneous projective bundles over abelian varieties

2011-04-05

arxiv.org/abs/1104.0818v2

Mathematics

Algebraic Geometry

Results generalized to most characteristics; additional details on the Brauer group; 32 pages

Scientific paper

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.

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