Very stable extensions on arithmetic surfaces

2010/09/30 by Christophe, Soulé
#14G40 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1009.6191

Abstract

Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E. From this result we deduce new inequalities for the successive minima of the euclidean lattice H¹(X,L^-1), where L is an hermitian line bundle on the arithmetic surface X.

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