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 Mosc. Math. J., 2017, Volume 17, Number 2, Pages 291–321 (Mi mmj638)

Deformations of the Hilbert scheme of points on a del Pezzo surface

Chunyi Li

School of Mathematics and Maxwell Institute, University of Edinburgh

Abstract: Let $S$ be a smooth del Pezzo surface over $\mathbb C$ of degree $d$ and $\mathrm{Hilb}^nS$ be the Hilbert scheme that parameterizes $0$-dimensional subschemes of length $n$. In this paper, we construct a flat family of deformations of $\mathrm{Hilb}^nS$ which can be conceptually understood as the Hilbert scheme of deformed non-commutative del Pezzo surfaces. Further we show that each deformed $\mathrm{Hilb}^nS$ carries a generically symplectic holomorphic Poisson structure. Moreover, the generic deformation of $\mathrm{Hilb}^nS$ has an $(11-d)$-dimensional moduli space and each of the fibers is of the form that we construct.

Key words and phrases: Hilbert scheme, exceptional collection, geometric invariant theory, holomorphic Poisson structure.

Full text: http://www.mathjournals.org/.../2017-017-002-006.html
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Document Type: Article
MSC: 14D20, 16E35
Received: July 29, 2014; in revised form January 20, 2016
Language: English

Citation: Chunyi Li, “Deformations of the Hilbert scheme of points on a del Pezzo surface”, Mosc. Math. J., 17:2 (2017), 291–321

Citation in format AMSBIB
\Bibitem{Li17} \by Chunyi~Li \paper Deformations of the Hilbert scheme of points on a~del Pezzo surface \jour Mosc. Math.~J. \yr 2017 \vol 17 \issue 2 \pages 291--321 \mathnet{http://mi.mathnet.ru/mmj638} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3669875}