Since the late 1960s, methods of birational geometry have been used successfully in the
theory of linear algebraic groups, especially in arithmetic problems. This book--which can be …

arXiv:alg-geom/9510014v1 26 Oct 1995 Page 1 arXiv:alg-geom/9510014v1 26 Oct 1995
Manin’s conjecture for toric varieties Victor V. Batyrev∗ Universität-GHS-Essen, Fachbereich …

Notre but, dans ce mémoire, est double. Nous étendons tout d'abord la théorie de
l'intersection arithmétique de Gillet-Soulé afin qu'elle englobe les fibres en droites …

Let ${\cal L}=(L,\|\cdot\| _v) $ be an ample metrized invertible sheaf on a smooth quasi-
projective algebraic variety $ V $ defined over a number field. Denote by $ N (V,{\cal L}, B) …

We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space
via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms …

We consider some families of smooth Fano hypersurfaces $ X_ {n+ 2} $ in ${\bf P}^{n+
2}\times {\bf P}^ 3$ given by a homogeneous polynomial of bidegree $(1, 3) $. For these …

For a locally compact second countable group G and a lattice subgroup Γ, we give an
explicit quantitative solution of the lattice point counting problem in general domains in G …

Si V est une variété algébrique projective sur un corps de nombres dont les points rationnels
sont denses pour la topologie de Zariski, il est naturel de munir V d'une hauteur et d'étudier …

We establish asymptotic formulas for volumes of height balls in analytic varieties over local
fields and in adelic points of algebraic varieties over number fields, relating the Mellin …

We investigate analytic properties of height zeta functions of toric varieties. Using the height
zeta functions, we prove an asymptotic formula for the number of rational points of bounded …