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Notes on questions of W. Vogel concerning the converse to Bézout's theorem

Published online by Cambridge University Press:  20 January 2009

Thilo Pruschke
Thilo Pruschke
Affiliation:
Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, D 06099 Halle/s, Germany
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Abstract

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Lazarsfeld proved a bound for the excess dimension of an intersection of irreducible and reduced schemes. Flenner and Vogel gave another approach for reduced, non-degenerate schemes which are connected in codimension one, using the intersection algorithm of Stückrad and Vogel and defining a new multiplicity k. Renschuch and Vogel considered a condition to ensure that there is no degeneration for more than two schemes. We define an integer which enables us to unify these methods. This allows us to generalize the result of Flenner and Vogel to non-reduced schemes by comparing the multiplicities j and k. Using this point of view we give applications to converses of Bézout's theorem; in particular we investigate the Cohen-Macaulay case.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 3 , October 1993 , pp. 427 - 445
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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