English

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

R2 v1 2026-07-22T17:21:26.757Z