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Some algebraic consequences of Green's hyperplane restriction theorems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-9961-383X
2010 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 214, no 7, 1263-1270 p.Article in journal (Refereed) Published
Abstract [en]

We discuss Green's paper [11] from a new algebraic perspective, and provide applications of its results to level and Gorenstein algebras, concerning their Hilbert functions and the weak Lefschetz property. In particular, we will determine a new infinite class of symmetric h-vectors that cannot be Gorenstein h-vectors, which was left open in the recent work [19]. This includes the smallest example, previously unknown, h = (1, 10, 9, 10, 1). As M. Green's results depend heavily on the characteristic of the base field, so will ours. The Appendix contains a new argument, kindly provided to us by M. Green, for Theorems 3 and 4 of [11], since we had found a gap in the original proof of those results during the preparation of this manuscript.

Place, publisher, year, edition, pages
2010. Vol. 214, no 7, 1263-1270 p.
Keyword [en]
gorenstein artin-algebras, hilbert-functions, generic forms, weak, codimension, property
National Category
URN: urn:nbn:se:kth:diva-19254DOI: 10.1016/j.jpaa.2009.10.010ISI: 000274938600021ScopusID: 2-s2.0-74849090344OAI: diva2:337301
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-21Bibliographically approved

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