We study the integral points on , where is the branch locus of a projection from a hypersurface in to a hyperplane . We extend to the general case a result by Zannier (whose approach we follow) and we also obtain a sharper bound that yields, in some cases, the finiteness of integral points. The results presented are effective and the proofs provide a way to actually construct a set containing all the integral points in question. Thus, there are concrete applications to the study of Diophantine equations, more precisely to the problem of finding integral solutions to equations , where is a given nonzero value and is a homogeneous form defining the branch locus , i.e. a discriminant.
Cite this article
Andrea Ciappi, Integral points on the complement of the branch locus of projections from hypersurfaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 2, pp. 277–291DOI 10.4171/RLM/762