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arXiv · 1104.0818

Homogeneous projective bundles over abelian varieties

Michel Brion
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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.

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Michel Brion. 2013-03-16. Homogeneous projective bundles over abelian varieties. https://doi.org/10.2140/ant.2013.7.2475

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