Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T15:57:04.685Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected]
JERZY WEYMAN
Affiliation:
Department of Mathematics, Northeastern University, Boston, MA 02115, [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)