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The Positivity of Intersection Multiplicities and Symbolic Powers of Prime Ideals |
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| Authors: | Kazuhiko Kurano Paul C Roberts |
| Affiliation: | (1) Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo, 192-0397, Japan;(2) Department of Mathematics, University of Utah, Salt Lake City, Utah, 84112, U.S.A. |
| Abstract: | 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 conjecture symbolic power regular local ring intersection multiplicity |
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