Semi-stable extensions on arithmetic surfaces

Details Semi-stable extensions on arithmetic surfaces Semi-stable extensions on arithmetic surfaces

2005-05-04

arxiv.org/abs/math/0505079v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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