An intersection number for the punctual Hilbert scheme of a surface
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.alg-geom/9603015,
title = {An intersection number for the punctual Hilbert scheme of a surface},
author = {Geir Ellingsrud and Stein Arild Strømme},
journal= {arXiv preprint arXiv:alg-geom/9603015},
year = {2008}
}
Comments
AMSLaTeX v 1.2, 7 pages