Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal families of Gorenstein algebras


Author: Jan O. Kleppe
Journal: Trans. Amer. Math. Soc. 358 (2006), 3133-3167
MSC (2000): Primary 14C05, 13D10, 13D03, 13D07, 13C40
Published electronically: January 24, 2006
MathSciNet review: 2216262
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to study maximal irreducible families of Gorenstein quotients of a polynomial ring $ R$. Let $ \operatorname{GradAlg}^H(R)$ be the scheme parametrizing graded quotients of $ R$ with Hilbert function $ H$. We prove there is a close relationship between the irreducible components of $ \operatorname{GradAlg}^H(R)$, whose general member is a Gorenstein codimension $ (c+1)$ quotient, and the irreducible components of $ \operatorname{GradAlg}^{H'}(R)$, whose general member $ B$ is a codimension $ c$ Cohen-Macaulay algebra of Hilbert function $ H'$ related to $ H$. If the Castelnuovo-Mumford regularity of the Gorenstein quotient is large compared to the Castelnuovo-Mumford regularity of $ B$, this relationship actually determines a well-defined injective mapping from such ``Cohen-Macaulay'' components of $ \operatorname{GradAlg}^{H'}(R)$ to ``Gorenstein'' components of $ \operatorname{GradAlg}^{H}(R)$, in which generically smooth components correspond. Moreover the dimension of the ``Gorenstein'' components is computed in terms of the dimension of the corresponding ``Cohen-Macaulay'' component and a sum of two invariants of $ B$. Using linkage by a complete intersection we show how to compute these invariants. Linkage also turns out to be quite effective in verifying the assumptions which appear in a generalization of the main theorem.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14C05, 13D10, 13D03, 13D07, 13C40

Retrieve articles in all journals with MSC (2000): 14C05, 13D10, 13D03, 13D07, 13C40


Additional Information

Jan O. Kleppe
Affiliation: Faculty of Engineering, Oslo University College, Postboks 4, St. Olavs plass, N-0130 Oslo, Norway
Email: JanOddvar.Kleppe@iu.hio.no

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03845-1
PII: S 0002-9947(06)03845-1
Keywords: Parametrization, Gorenstein algebra, Artinian algebra, liaison, licci, Cohen-Macaulay, canonical module, normal module, Hilbert scheme.
Received by editor(s): August 13, 2004
Published electronically: January 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society