Very stable extensions on arithmetic surfaces

Details Very stable extensions on arithmetic surfaces Very stable extensions on arithmetic surfaces

2010-09-30

arxiv.org/abs/1009.6191v2

Mathematics

Algebraic Geometry

This paper has been withdrawn since both theorems claimed in it are incorrect

Scientific paper

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 H^1(X,L^{-1}), where L is an hermitian line bundle on the arithmetic surface X.

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