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Weakly normal varieties: The multicross singularity and some vanishing theorems on local cohomology

Published online by Cambridge University Press:  22 January 2016

John V. Leahy  and
Marie A. Vitulli
John V. Leahy
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403, USA
Marie A. Vitulli
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403, USA
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The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieties”, where the historical framework and fundamental properties of weakly normal varieties were presented in detail. Here we devote our attention to the study of the multicross singularity and the role of local cohomology in the theory of weakly normal varieties.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 83 , October 1981 , pp. 137 - 152
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[1] Adkins, W. A. and Leahy, J. V., A topological criterion for local optimality of weakly normal complex spaces, Math. Ann., 243 (1979), 115–123.Google Scholar
[2] Endô, S., Projective modules over polynomial rings, J. Math. Soc. Japan, 15 (1963), 339–352.Google Scholar
[3] Hartshorne, R., Algebraic Geometry, Springer GTM 52, New York, 1977.Google Scholar
[4] Iverson, B., Generic Local Structure in Commutative Algebra, Springer LNM 310, Berlin (1973).Google Scholar
[5] Leahy, J. V. and Vitulli, M. A., Seminormal rings and weakly normal varieties, Nagoya Math. J., 82 (1981), 27–56.Google Scholar
[6] Matsumura, H., Commutative Algebra, W. A. Benjamin, New York, 1970.Google Scholar