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Cohen–Macaulay Properties of Thom–Boardman Strata I: Morin's Ideal
Author(s) -
Fukui Toshizumi,
Weyman Jerzy
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012181
Subject(s) - morin , mathematics , iterated function , pure mathematics , norm (philosophy) , ideal (ethics) , jacobian matrix and determinant , algebra over a field , mathematical analysis , epistemology , medicine , philosophy , pathology
Thom–Boardman strata σ I are fundamental tools in studying singularities of maps. The Zariski closures of the strata σ I are components of the set of zeros of the ideals Δ I defined by B. Morin using iterated jacobian extensions in his paper ‘Calcul jacobien’ ( Ann. Sci. École Norm. Sup. } 8 (1975) 1–98). In this paper, we consider the question of when the Morin ideals Δ I define Cohen–Macaulay spaces. We determine all I =( i 1 ,…, i k ) such that Δ I defines a Cohen–Macaulay space alongthe Σ i 1stratum. 1991 Mathematics Subject Classification : 13D25, 14B05, 14M12, 58C25.
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