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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A special case of positivity (II)


Author: S. P. Dutta
Journal: Proc. Amer. Math. Soc. 133 (2005), 1891-1896
MSC (2000): Primary 13H05, 14C17; Secondary 13D15, 14H15
Published electronically: February 24, 2005
MathSciNet review: 2137852
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Abstract: In this note we prove the following special case of Serre's conjecture on Intersection Multiplicity: Let $(R,m)$ be a regular local ring and let $P$, $Q$ be two prime ideals such that $\ell (R/(P+Q))<\infty $, $\dim R/P +\dim R/Q=\dim R$ and dimension of $G_{m}(R/P)\otimes _{G_{m}(R)}G_{m}(R/Q)<2$. Then $\chi (R/P,R/Q)\geq e_{m}(R/P) e_{m}(R/Q)$; here $e_{m}(T)$ denotes the Hilbert-Samuel multiplicity for any finitely generated module $T$ with respect to $m$.


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Additional Information

S. P. Dutta
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: dutta@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07929-3
PII: S 0002-9939(05)07929-3
Keywords: Regular local ring, Hilbert multiplicity, intersection multiplicity, blow-up, Chow-group, Riemann-Roch Theorem
Received by editor(s): September 12, 2003
Received by editor(s) in revised form: February 17, 2004
Published electronically: February 24, 2005
Additional Notes: This research was partially supported by NSF grant DMS 99-70263.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.