Journal of the Mathematical Society of Japan

Relative Hilbert scheme of points

Iman SETAYESH

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Abstract

Let $D$ be a smooth divisor on a non singular surface $S$. We compute the Betti numbers of the Hilbert scheme of points of $S$ relative to $D$. In the case of $\mathbb{P}^2$ and a line in it, we give an explicit set of generators and relations for the corresponding cohomology groups.

Article information

Source
J. Math. Soc. Japan Volume 68, Number 3 (2016), 1325-1356.

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956170

Digital Object Identifier
doi:10.2969/jmsj/06831325

Mathematical Reviews number (MathSciNet)
MR3523549

Zentralblatt MATH identifier
06642415

Subjects
Primary: 14C05: Parametrization (Chow and Hilbert schemes)
Secondary: 14J10: Families, moduli, classification: algebraic theory

Keywords
Hilbert scheme of points relative Hilbert scheme

Citation

SETAYESH, Iman. Relative Hilbert scheme of points. J. Math. Soc. Japan 68 (2016), no. 3, 1325--1356. doi:10.2969/jmsj/06831325. https://projecteuclid.org/euclid.jmsj/1468956170.


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