Algebra & Number Theory

Homogeneous projective bundles over abelian varieties

Michel Brion

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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.

Article information

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

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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]

abelian varieties projective bundles Heisenberg groups Brauer group


Brion, Michel. Homogeneous projective bundles over abelian varieties. Algebra Number Theory 7 (2013), no. 10, 2475--2510. doi:10.2140/ant.2013.7.2475.

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