Relative Hilbert Scheme of Points

Iman Setayesh

doi:10.2969/jmsj/06831325

Relative Hilbert Scheme of Points

Algebraic Geometry 2018-05-01 v2

Authors: Iman Setayesh

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Abstract

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

Keywords

hilbert scheme hilbert functions algebraic surfaces

Cite

@article{arxiv.1006.0011,
  title  = {Relative Hilbert Scheme of Points},
  author = {Iman Setayesh},
  journal= {arXiv preprint arXiv:1006.0011},
  year   = {2018}
}

Comments

The final version has been published in the Journal of the Mathematical Society of Japan

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