Cohen-Macaulay Properties of Thom-Boardman Strata I: Morin's Ideal

Thom–Boardman strata ^I are fundamental tools in studyingsingularities of maps. The Zariski closures of the strata ^Iare components of the set of zeros of the ideals ^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 questionof when the Morin ideals ^I define Cohen–Macaulay spaces.We determine all I=(i₁...,i_k) such that ^I defines a Cohen–Macaulayspace alongthe stratum. 1991 Mathematics Subject Classification: 13D25, 14B05, 14M12, 58C25.