A Riemann-Roch formula for the blow-up of a nonsingular affine scheme

C. Y.Jean Chan, Claudia Miller

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

The main purpose of this paper is to obtain the Hilbert-Samuel polynomial of a module via blowing up and applying intersection theory rather than employing associated graded objects. The result comes in the form of a concrete Riemann-Roch formula for the blow-up of a nonsingular affine scheme at its closed point. To achieve this goal, we note that the blow-up sits naturally between two projective spaces, one over a field and one a regular local ring, and then apply the Grothendieck-Riemann-Roch Theorem to each containment.

Original languageEnglish (US)
Pages (from-to)3003-3025
Number of pages23
JournalJournal of Algebra
Volume322
Issue number9
DOIs
StatePublished - Nov 1 2009

Keywords

  • Blow-up
  • Hilbert-Samuel polynomial
  • Riemann-Roch theorem

ASJC Scopus subject areas

  • Algebra and Number Theory

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