Homogeneous projective bundles over abelian varieties
Algebraic Geometry
2016-01-20 v4
Abstract
We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of commutative algebraic groups; the irreducible bundles correspond to Heisenberg groups and their standard representations. Our results extend those of Mukai on semi-homogeneous vector bundles, and yield a geometric view of the Brauer group of abelian varieties.
Cite
@article{arxiv.1104.0818,
title = {Homogeneous projective bundles over abelian varieties},
author = {Michel Brion},
journal= {arXiv preprint arXiv:1104.0818},
year = {2016}
}
Comments
Final version, accepted for publication in Algebra and Number Theory Journal; 37 pages. This is a slightly shortened version of v3: Section 6 has been suppressed as well as the proofs of Propositions 4.1 and 4.2; Section 4 has been relegated to the very end