Slope-determinant method, complex cellular structures and hypersurface
coverings of regular rational points
Slope-determinant method, complex cellular structures and hypersurface
coverings of regular rational points
We use the determinant method of Bombieri-Pila and Heath-Brown and its Arakelov reformulation by Chen utilizing Bost's slope method to estimate the number of hypersurfaces required to cover the regular rational points with bounded Arakelov height on a projective variety. Using complex cellular structures introduced by Binyamini-Novikov, we replace the …