Invariant d'Hermite des jacobiennes de graphes pond\'{e}r\'{e}s
Combinatorics
2007-11-27 v1 Metric Geometry
Number Theory
Abstract
To any weighted graph of first Betti number b is naturally associated a lattice of dimension b, definite in a similar way that the jacobian for a Riemann surface. This class of lattices generated by graphs is particularly interesting. We show here an upperbound of the Hermite invariant of such a lattice according to b whose order is ln b. This order is optimal : it is realized by the Hermite invariant of the jacobian of a systolicly economic graph.
Keywords
Cite
@article{arxiv.math/0506616,
title = {Invariant d'Hermite des jacobiennes de graphes pond\'{e}r\'{e}s},
author = {Florent Balacheff},
journal= {arXiv preprint arXiv:math/0506616},
year = {2007}
}
Comments
9 pages