English

Semi-stable extensions on arithmetic surfaces

Algebraic Geometry 2007-05-23 v1

Abstract

On a given arithmetic surface, inspired by work of Miyaoka, we consider vector bundles which are extensions of a line bundle by another one. We give sufficient conditions for their restriction to the generic fiber to be semi-stable. We then apply the arithmetic analog of Bogomolov inequality in Arakelov theory, and deduce from it a lower bound for some successive minima in the lattice of extension classes between these line bundles.

Keywords

Cite

@article{arxiv.math/0505079,
  title  = {Semi-stable extensions on arithmetic surfaces},
  author = {C. Soule},
  journal= {arXiv preprint arXiv:math/0505079},
  year   = {2007}
}