Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587403 | Journal of Algebra | 2009 | 23 Pages |
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.
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