Examples of factorial threefolds complete intersection in mathbbP5{mathbb{P}^5} with many singularities

摘要

Denote by ν _m (d) the maximal integer for which there exists for a threefold complete intersection of hypersurfaces of degree respectively d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = ν _m (d). We prove that, where asymptotically. This result extends (Di Gennaro and Franco in Commun Contemp Math 10(5):745–764, 2008, Corollary 2.10).