Complements of hyperplane sub-bundles in projective space bundles over the projective line
Algebraic Geometry
2011-09-01 v1
Abstract
We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection of H . In particular it depends neither on the ambient bundle nor on a particular ample hyperplane sub-bundle with given r-fold self-intersection. Our proof exploits the unexpected property that every such complement comes equipped with the structure of a non trivial torsor under a vector bundle on the affine line with a double origin.
Cite
@article{arxiv.1108.6209,
title = {Complements of hyperplane sub-bundles in projective space bundles over the projective line},
author = {Adrien Dubouloz},
journal= {arXiv preprint arXiv:1108.6209},
year = {2011}
}