Normal Projective Varieties of Degree 5

Abstract

We list all the irreducible reduced and not degenerate normal projective varieties X ⊂ P N k of dimension n and degree five defined over an algebraically closed field k of char(k) = 0. In the smooth case, or when n = 2, we give also classification results for any algebraically closed field k of char(k) ≥ 0.