Journal of the Mathematical Society of Japan

Relative Hilbert scheme of points


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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.

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

First available in Project Euclid: 19 July 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hilbert scheme of points relative Hilbert scheme


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

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