Positive integral points on Mordell-Schinzel surfaces
Antoine de Saint Germain, Robin Zhang
Abstract
We apply the theory of generalised cluster algebras to classify the finiteness of positive integral points on the class of log K3 surfaces defined by xyz = G(x,y) where G has positive coefficients. We furthermore establish results on Zariski density, number of orbits and asymptotic growth of such points. These provide a Diophantine realisation of the finite-affine-indefinite trichotomy of rank-two root systems.
Create a lesson
Related papers
Rational points on loxodromic K3 surfaces and complex dynamics
Damián Gvirtz-Chen, Zhizhong Huang, Zhuchao Ji et al.
Ramanujan-type congruences for the smallest parts function
Larry Rolen
Some instances of modularity for residually reducible representations in the mixed case
Luis V. Dieulefait
Classification of torsion of elliptic curves over sextic fields
Filip Najman
A generalization of the Dirichlet approximation theorem for affine actions on the real line
Mohammad Javaheri
On ill-distributed B3 and B4 sets
André Hisatsuga, Rafael Miyazaki, Cosmin Pohoata