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COHEN–MACAULAY PROPERTIES OF THOM–BOARDMAN STRATA I: MORIN'S IDEAL

Published online by Cambridge University Press:  01 March 2000

TOSHIZUMI FUKUI  and
JERZY WEYMAN
TOSHIZUMI FUKUI
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo, Urawa 338-8570, Japantfukui@rimath.saitama-u.ac.jp
JERZY WEYMAN
Affiliation:
Department of Mathematics, Northeastern University, Boston, MA 02115, USAweyman@neu.edu
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Abstract

Thom--Boardman strata $\Sigma^I$ are fundamental tools in studying singularities of maps. The Zariski closures of the strata $\Sigma^I$ are components of the set of zeros of the ideals $\Delta^I$ defined by B. Morin using iterated jacobian extensions in his paper `Calcul jacobien' ({\em Ann. Sci. \'Ecole Norm. Sup.} 8 (1975) 1--98). In this paper, we consider the question of when the Morin ideals $\Delta^I$ define Cohen--Macaulay spaces. We determine all $I=(i_1,...,i_k)$ such that $\Delta^I$ defines a Cohen--Macaulay space alongthe $\Sigma^{i_1}$ stratum. 1991 Mathematics Subject Classification: 13D25, 14B05, 14M12, 58C25.

Keywords

Thom--Boardman strataMorin's idealCohen--Macaulay propertySchur functorgeometric technique of calculating syzygies
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 80 , Issue 2 , March 2000 , pp. 257 - 303
Copyright
2000 London Mathematical Society

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