Injections into Affine Hypersurfaces

摘要

Let X be a smooth affine variety of dimension n > 2. Assume that the group H_1 (X,Z) is a torsion group and that χ(X) = 1. Let Y be a projectively smooth affine hypersurface Y　 is contained in C~(n+1) of degree d > 1, which is smooth at infinity. Then there is no injective polynomial mapping f:X → Y. This contradicts a result of Peretz [5].