English

Very stable extensions on arithmetic surfaces

Algebraic Geometry 2011-05-17 v2 Number Theory

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

Keywords

Cite

@article{arxiv.1009.6191,
  title  = {Very stable extensions on arithmetic surfaces},
  author = {Soulé Christophe},
  journal= {arXiv preprint arXiv:1009.6191},
  year   = {2011}
}

Comments

This paper has been withdrawn since both theorems claimed in it are incorrect

R2 v1 2026-06-21T16:21:50.144Z