Finiteness and Density Problems for (Positive) Integral Points on Mordell–Schinzel Surfaces

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IHES

Séminaire de géométrie arithmétique In 1952, Mordell erroneously claimed that the surface xyz = G(x,y) has infinitely many integral points for any G ∈ ℤ [x,y]. I will discuss a classification for finiteness and Zariski density of (positive) integral points on these log K3 surfaces when the coefficients of G are non-negative. This combines a dynamical argument proposed by Mordell, the theory of gen

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