Théorie de Voronoi géométrique. - Propriétés de finitude pour les familles de réseaux et analogues

摘要

A geometric Voronoi's theory is developed and applied to classical families of euclidean lattices (such as symplectic or orthogonal lattices). In particular, new finiteness results are obtained concerning configurations of minimal vectors and special lattices (for example the perfect ones) in these families. The geometric methods introduced are also illustrated by the study of related objects (Humbert forms) or similar ones (Riemann surfaces).