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A special case of positivity (II)

Authors:	S P Dutta

Institution:	Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801

Abstract:	In this note we prove the following special case of Serre's conjecture on Intersection Multiplicity: Let be a regular local ring and let , 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 with respect to .

Keywords:	Regular local ring Hilbert multiplicity intersection multiplicity blow-up Chow-group Riemann-Roch Theorem

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