Hilbert Series and Lefschetz Properties of Dimension One Almost Complete Intersections. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Dimca, Alexandru; Popescu, Dorin
• Is Part Of: Communications in algebra. Volume 44:Issue 10(2016)
• Page Start: 4467
• Page End: 4482
• Publication Date: 2016-10-02
• Subjects: Almost complete intersections -- Isolated singularities -- Lefschetz property -- Projective hypersurfaces; Primary: 13D40 -- Secondary: 14B05 -- 14C20 -- 13D02; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1087535
• Languages: English
• ISSNs: 0092-7872

Abstract

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.