An intersection number for the punctual Hilbert scheme of a surface

Details An intersection number for the punctual Hilbert scheme of a surface An intersection number for the punctual Hilbert scheme of a surface

1996-03-21

arxiv.org/abs/alg-geom/9603015v1

Mathematics

Algebraic Geometry

AMSLaTeX v 1.2, 7 pages

Scientific paper

Let S be a smooth projective surface, and consider the following two subvarieties of the Hilbert scheme parameterizing closed subschemes of S of length n: A = {subschemes with support in a fixed point of S} B = {subschemes with support in one (variable) point of S} A and B have complementary dimensions in the Hilbert scheme. We prove that the intersection number [A].[B] = n(-1)^(n-1), answering a question by H. Nakajima.

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