Diophantine problems under birational quadratic transformations between two planes (Q762569)

Let \(\pi\) (x,y) and \(\pi\) '(x',y') be two affine planes and let \(T: \pi \to \pi '\) be a birational quadratic transformation given by equations: \(x'=F_ 1(x,y)/F_ 3(x,y),\quad y'=F_ 2(x,y)/F_ 3(x,y),\) where \(F_ 1,F_ 2,F_ 3\) are polynomials of degree 2 with integer coefficients. In particular, let \(C_ 3\) be the conic of equation \(F_ 3(x,y)=0.\) The author studies the configuration of the ''bi-integer'' points (i.e. integer points of \(\pi\) mapping to integer points of \(\pi\) ') and obtains a minute classification of integral birational quadratic transformations depending on the structure of \(C_ 3\). - The proof is based on classical results about the conics. The analogous problem for homographies has been studied by the same author in two previous papers.