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Cohen–Macaulay Properties of Thom–Boardman Strata II: the Defining Ideals of Σi, j

Published online by Cambridge University Press:  25 June 2003

Toshizumi Fukui  and
Jerzy Weyman
Toshizumi Fukui
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo, Saitama 338-8570, Japan. E-mail: tfukui@rimath.saitama-u.ac.jp
Jerzy Weyman
Affiliation:
Department of Mathematics, Northeastern University, Boston, MA 02115, USA. E-mail: weyman@neu.edu
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Abstract

We consider the Zariski closure of Thom–Boardman strata $\Sigma^{i, j}$ in the jet space for map-germs $(\mathbf{C}^n, 0)\to(\mathbf{C}^p, 0)$. We apply the geometric technique of calculating syzygies to the desingularization of $\Sigma^{i, j}$ constructed by Ronga. We investigate when the normalization of the coordinate ring of $\Sigma^{i, j}$ is rational in the cases $i = n - p + 1$ or $i = j = 1$. We also consider when these coordinate rings are normal with rational singularities.

Keywords

Thom–Boardman strataRonga's desingularizationrational singularitygeometric technique of calculating syzygies13D0214B0514M0514M1258C25 (primary)58K20 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 1 , July 2003 , pp. 137 - 163
Copyright
2003 London Mathematical Society

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Footnotes

This research was done when the second-named author was visiting Saitama University. The authors warmly acknowledge the partial support of a Grant-in-Aid for Scientific Research and an NSF grant.