Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 10 (2013), 2475-2510.
Homogeneous projective bundles over abelian varieties
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.
Algebra Number Theory, Volume 7, Number 10 (2013), 2475-2510.
Received: 17 September 2012
Revised: 31 January 2013
Accepted: 12 March 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14K05: Algebraic theory
Secondary: 14F22: Brauer groups of schemes [See also 12G05, 16K50] 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Brion, Michel. Homogeneous projective bundles over abelian varieties. Algebra Number Theory 7 (2013), no. 10, 2475--2510. doi:10.2140/ant.2013.7.2475. https://projecteuclid.org/euclid.ant/1513730114