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The Positivity of Intersection Multiplicities and Symbolic Powers of Prime Ideals

Published online by Cambridge University Press:  04 December 2007

Kazuhiko Kurano  and
Paul C. Roberts
Kazuhiko Kurano
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan. E-mail: kurano@math.metro-u.ac.jp
Paul C. Roberts
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, U.S.A. E-mail: Roberts@math.utah.edu
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Abstract

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Serre's nonnegativity conjecture for intersection multiplicities has recently been proven by O. Gabber. In this paper we investigate Serre's positivity conjecture using the methods which he developed. We show in particular that the positivity conjecture has implications for properties of symbolic powers of prime ideals in regular local rings.

Keywords

Serre's positivity conjecturesymbolic powerregular local ringintersection multiplicity
Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 2 , June 2000 , pp. 165 - 182
Copyright
© 2000 Kluwer Academic Publishers