Open Access
2013 Homogeneous projective bundles over abelian varieties
Michel Brion
Algebra Number Theory 7(10): 2475-2510 (2013). DOI: 10.2140/ant.2013.7.2475


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.


Download Citation

Michel Brion. "Homogeneous projective bundles over abelian varieties." Algebra Number Theory 7 (10) 2475 - 2510, 2013.


Received: 17 September 2012; Revised: 31 January 2013; Accepted: 12 March 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1315.14057
MathSciNet: MR3194649
Digital Object Identifier: 10.2140/ant.2013.7.2475

Primary: 14K05
Secondary: 14F22 , 14J60 , 14L30

Keywords: abelian varieties , Brauer group , Heisenberg groups , projective bundles

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 10 • 2013
Back to Top