Homogeneous projective bundles over abelian varieties

Brion, Michel

doi:10.2140/ant.2013.7.2475

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Homogeneous projective bundles over abelian varieties

Michel Brion

Vol. 7 (2013), No. 10, 2475–2510

DOI: 10.2140/ant.2013.7.2475

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

Vol. 7, No. 10, 2013