Erratum : Linear projections and successive minima

TL;DR

This paper corrects a previous incorrect proof by establishing a new relationship between the height of a curve in projective space and the successive minima of an associated Euclidean lattice.

Contribution

It provides a new proven result linking lattice minima to geometric heights, replacing an earlier flawed proof.

Findings

Established a valid relation between lattice minima and curve height

Corrected the theoretical understanding in the previous work

Provides a new proof for the relationship

Abstract

Given a euclidean lattice and a curve in the corresponding projective space, our goal is to relate the height of the curve to the successive minima of the lattice. The proof of such a statement in http://hal.archves-ouvertes.vf/hal-00270564 was incorrect. We prove another result instead.