A special case of positivity (II)

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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 l(R/(P + Q)) < ∞, dim A/P + dim R/Q = dim R and dimension of G m(R/P) ⊗ Gm(R) G m(R/Q) < 2. Then Χ(R/P,R/Q} ≥ 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.

Original languageEnglish (US)
Pages (from-to)1891-1896
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - Jul 2005


  • Blow-up
  • Chow-group
  • Hilbert multiplicity
  • Intersection multiplicity
  • Regular local ring
  • Riemann-Roch Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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