2005/05/04 by C. Soule, Soule, C.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #MSC 14G40 #math.AG #msc:14G40
paper · pdf · doi:10.48550/arxiv.math/0505079
arxiv created 2005/05/04 · arxiv updated 2009/12/01
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.