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Hilbert series of residual intersections

Part of: Special varieties Commutative algebra: Homological methods Projective and enumerative geometry Local rings and semilocal rings Theory of modules and ideals Cycles and subschemes

Published online by Cambridge University Press:  09 June 2015

Marc Chardin ,
David Eisenbud  and
Bernd Ulrich
Marc Chardin
Affiliation:
Institut de Mathématiques de Jussieu, CNRS and UPMC, 4 place Jussieu, 75005 Paris, France email [email protected]
David Eisenbud
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA email [email protected]
Bernd Ulrich
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA email [email protected]
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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.

Keywords

residual intersectionHilbert seriesmultiplicityHilbert coefficientsconormal modulessecant varieties

MSC classification

Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13C40: Linkage, complete intersections and determinantal ideals
Secondary: 13H15: Multiplicity theory and related topics 14M06: Linkage 14C17: Intersection theory, characteristic classes, intersection multiplicities 14N15: Classical problems, Schubert calculus
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 9 , September 2015 , pp. 1663 - 1687
Copyright
© The Authors 2015 

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