The Chow of $S^{[n]}$ and the universal subscheme

Andrei Neguţ

The Chow of $S^{[n]}$ and the universal subscheme

Algebraic Geometry 2020-08-18 v2

Authors: Andrei Neguţ

Abstract

We prove that any element in the Chow ring of the Hilbert scheme $\text{Hilb}_n$ of $n$ points on a smooth surface $S$ is a universal class, i.e. the pushforward of a polynomial in the Chern classes of the universal subscheme on $\text{Hilb}_n \times S^k$ for some $k \in \mathbb{N}$ , with coefficients pulled back from the Chow of $S^k$ .

Keywords

chow ring hilbert scheme universal subscheme chern classes smooth surface

Cite

@article{arxiv.1912.03287,
  title  = {The Chow of $S^{[n]}$ and the universal subscheme},
  author = {Andrei Neguţ},
  journal= {arXiv preprint arXiv:1912.03287},
  year   = {2020}
}

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