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Multiplicity and t-isomultiple ideals

Published online by Cambridge University Press:  22 January 2016

M.E. Rossi  and
G. Valla
M.E. Rossi
Affiliation:
Dipartimento di Matematica, Università di Genova, 16132 Genova, Italy
G. Valla
Affiliation:
Dipartimento di Matematica, Università di Genova, 16132 Genova, Italy
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Let V be an irreducible non degenerate variety in Pn; a classical geometric result says that degree (V) ≥ codim V + 1 and, if equality holds, V is said to be of minimal degree. Varieties of minimal degree has been classified by Del Pezzo and Bertini and they all are intersections of quadrics. The local version of this result is due to J. Sally who proved that if is a regular local ring and is a Cohen-Macaulay local ring of minimal multiplicity, according to the bound e(R) ≥ height (I) + 1 given by Abhyankar, then the tangent cone of R is intersection of quadrics and it is Cohen-Macaulay.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 110 , June 1988 , pp. 81 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

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