On non-normal del Pezzo varieties

Two projective subvarieties of Pr are said to be projectively equivalent if they are identified by a coordinate change. Up to projective equivalence, varieties of minimal degree were completely classified more than one hundred years ago by P. del Pezzo and E. Bertini.As the next case, we study the same problem for del Pezzo varieties, focusing on the non-normal case of degree ⩾5. Note that the cases of degrees 3 and 4 were dealt with in Lee et al. (2011) [8], and Lee et al. (2012) [9], respectively. Our main result, Theorem 4.1, provides a complete classification of non-normal del Pezzo varieties of degree at least 5, up to projective equivalence.