An intersection number for the

punctual Hilbert scheme of a surface

Authors:
Geir Ellingsrud and Stein Arild Strømme

Journal:
Trans. Amer. Math. Soc. **350** (1998), 2547-2552

MSC (1991):
Primary 14C17, 14C05

MathSciNet review:
1432198

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Abstract | References | Similar Articles | Additional Information

Abstract: We compute the intersection number between two cycles and of complementary dimensions in the Hilbert scheme parameterizing subschemes of given finite length of a smooth projective surface . The -cycle corresponds to the set of finite closed subschemes the support of which has cardinality 1. The -cycle consists of the closed subschemes the support of which is one given point of the surface. Since is contained in , indirect methods are needed. The intersection number is , answering a question by H. Nakajima.

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Additional Information

**Geir Ellingsrud**

Affiliation:
Mathematical Institute, University of Oslo, P. O. Box 1053, N–0316 Oslo, Norway

Email:
ellingsr@math.uio.no

**Stein Arild Strømme**

Affiliation:
Mathematical Institute, University of Bergen, Johannes Brunsg. 12, N-5008 Bergen, Norway

Email:
stromme@mi.uib.no

DOI:
http://dx.doi.org/10.1090/S0002-9947-98-01972-2

Keywords:
Punctual Hilbert scheme,
intersection numbers

Received by editor(s):
September 1, 1996

Article copyright:
© Copyright 1998
American Mathematical Society