Hilbert Series and Lefschetz Properties of Dimension One Almost Complete Intersections. Issue 10 (2nd October 2016) - Dimca, Alexandru; Popescu, Dorin
Abstract : We generalize some results about the graded Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal J of dimension one. When the saturation I of J is a complete intersection, we get formulas for some invariants. Examples of hypersurfaces V : f = 0 in ℙ n whose Jacobian ideals J satisfy this property and with nontrivial Alexander polynomials are given in any dimension. A Lefschetz property for the graded quotient I / J is proved for n = 2 and a counterexample due to A. Conca is given for such a property when n = 3.