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 language | English |
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Pages (from-to) | 3003 - 3025 |
Journal | Journal of Algebra |
Volume | 322 |
Issue number | 9 |
State | Published - Nov 2009 |