Vol. 7, No. 10, 2013

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Homogeneous projective bundles over abelian varieties

Michel Brion

Vol. 7 (2013), No. 10, 2475–2510
Abstract

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

Keywords
abelian varieties, projective bundles, Heisenberg groups, Brauer group
Mathematical Subject Classification 2010
Primary: 14K05
Secondary: 14F22, 14J60, 14L30
Milestones
Received: 17 September 2012
Revised: 31 January 2013
Accepted: 12 March 2013
Published: 18 January 2014
Authors
Michel Brion
Institut Fourier
Université Grenoble I
CNRS UMR 5582
100 rue des Maths
BP 74
38402 St Martin d’Hères
France