Related papers: The Manin conjecture in dimension 2

We prove Manin's conjecture for four singular quartic del Pezzo surfaces over imaginary quadratic number fields, using the universal torsor method.

We prove a version of Manin's conjecture for a certain family of intrinsic quadrics, the base field being a global field of positive characteristic. We also explain how a very slight variation of the method we use allows to establish the…

This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…

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 quadratic fields, using universal torsors. Some of our tools…

By a heuristic argument, we relate two conjectures. One is a version of Manin's conjecture about the distribution of rational points on a Fano variety. We concern specific singular Fano varieties, namely quotients of projective spaces by…

We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank 1 and dimension at least 4 by analyzing the fibers of evaluation maps. As a corollary, we prove Geometric Manin's Conjecture in these cases.

The Manin conjecture is established for Ch\^atelet surfaces over Q arising as minimal proper smooth models of the surface Y^2+Z^2=f(X) where f is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not…

These lecture notes are meant to provide a pedagogical introduction, and present the latest theoretical and experimental developments on the physics of vortices in type II superconductors.

We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated…

Manin's relations characterize period polynomials of a modular form. In this paper, we propose a finite set of relations checked by bi-period polynomials of a couple of forms. Then we construct an Eisenstein part of depth 2 which…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

We construct first examples of singular del Pezzo surfaces with Zariski dense exceptional sets in Manin's conjecture, varying in degrees $1, 2$ and $3$. The obstructions arise from accumulating quasi-\'etale covers. We classify all…

We briefly summarise the current status of neutrino masses and mixing, paying special attention to the prospects for observing new leptonic interactions.

Manin's Conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Manin's Conjecture is a thin set.

Recent discoveries in the field of neutrino oscillations have provided a unique window into physics beyond the standard model. In this lecture, I summarize how well we understand the various observations, what they tell us about the nature…

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 example of a singular quartic del Pezzo surface that is an…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

In this paper, we prove a conjecture of Schnell in the surface case.

Inspired by a method of La Bret\`eche relying on some unique factorisation, we generalize work of Blomer, Br\"udern, and Salberger to prove Manin's conjecture in its strong form conjectured by Peyre for some infinite family of varieties of…

This pedagogical overview will cover the current status of neutrino physics from an experimentalist's point of view, focusing primarily on oscillation studies. The evidence for neutrino oscillations will be presented, along with the…