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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 26, Issue 2


Ideals of generalized invariants, local cohomology and Macaulay's double duality theorem

Larry Smith
Published Online: 2011-12-20 | DOI: https://doi.org/10.1515/form.2011.165


We show how to compute a Macaulay dual class in local cohomology H𝔪n(𝔽[V]) for an given ideal I(𝒮)𝔽[V] of generalized invariants associated to a set of reflections 𝒮GL(n,𝔽) that generate a finite subgroup G(𝒮)GL(n,𝔽). We then apply this in the case that the coinvariant algebra 𝔽[V]G(𝒮) is a fixed point free Poincaré duality algebra to obtain a Macaulay dual for the Hilbert ideal 𝔥(G(𝒮)) of G(𝒮).

Keywords: Invariant theory

MSC: 13D45; 13A50; 13C99; 51F15

About the article

Received: 2011-03-16

Revised: 2011-10-31

Published Online: 2011-12-20

Published in Print: 2014-03-01

Citation Information: Forum Mathematicum, Volume 26, Issue 2, Pages 497–521, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.165.

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