We classify all generalized del Pezzo surfaces (that is, minimal desingularizations of
singular del Pezzo surfaces containing only rational double points) whose universal torsors …

We determine which singular del Pezzo surfaces are equivariant compactifications of G_a^
2, to assist with proofs of Manin's conjecture for such surfaces. Additionally, we give an …

The central theme of this book is the study of rational points on algebraic varieties of Fano
and intermediate type--both in terms of when such points exist and, if they do, their …

A conjecture of Manin predicts the distribution of rational points on Fano varieties. We
provide a framework for proofs of Manin's conjecture for del Pezzo surfaces over imaginary …

Given an extension of number fields E⊂ F and a projective variety X over F, we compare the
problem of counting the number of rational points of bounded height on X with that of its Weil …

Inhomogeneous cubic congruences and rational points on del Pezzo surfaces Page 1 J. reine
angew. Math. 680 (2013), 69—151 DOI 10.1515/crelle.2012.039 Journal für die reine und …

We establish estimates for the number of solutions of certain affine congruences. These
estimates are then used to prove Manin's conjecture for a cubic surface split over ℚ whose …

We prove Manin's conjecture for two del Pezzo surfaces of degree four which are split over
Q and whose singularity types are respectively 3A_1 and A_1+ A_2. For this, we study a …

We establish Manin's conjecture for a cubic surface split over ℚ and whose singularity type
is 2A2+ A1. For this, we make use of a deep result about the equidistribution of the values of …

Some examples of curves countings on surfaces Let be a surface whose Cox ring has a
single relation satisfying moreover a kind of linearity property. We show that the geometric …