Hilbert series of residual intersections. (9th June 2015)

• Record Type: Journal Article
• Authors: Chardin, Marc; Eisenbud, David; Ulrich, Bernd
• Is Part Of: Compositio mathematica. Volume 151:Number 9(2015)
• Page Start: 1663
• Page End: 1687
• Publication Date: 2015-06-09
• Subjects: 13D40, -- 13C40 (primary), -- 13H15, -- 14M06, -- 14C17, -- 14N15 (secondary); residual intersection, -- Hilbert series, -- multiplicity, -- Hilbert coefficients, -- conormal modules, -- secant varieties; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X15007289
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We give explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper, we proved that such formulas should exist. We give applications to the number of equations defining projective varieties and to the dimension of secant varieties of surfaces and three-folds.