Automorphisms of Hilbert schemes of points on surfaces
Authors:
Pieter Belmans, Georg Oberdieck and Jørgen Vold Rennemo
Journal:
Trans. Amer. Math. Soc. 373 (2020), 6139-6156
MSC (2010):
Primary 14C05, 14J50
DOI:
https://doi.org/10.1090/tran/8106
Published electronically:
June 24, 2020
MathSciNet review:
4155174
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We show that every automorphism of the Hilbert scheme of $n$ points on a weak Fano or general type surface is natural, i.e., induced by an automorphism of the surface, unless the surface is a product of curves and $n=2$. In the exceptional case there exists a unique nonnatural automorphism. More generally, we prove that any isomorphism between Hilbert schemes of points on smooth projective surfaces, where one of the surfaces is weak Fano or of general type and not equal to the product of curves, is natural. We also show that every automorphism of the Hilbert scheme of $2$ points on $\mathbb {P}^n$ is natural.
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Additional Information
Pieter Belmans
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
MR Author ID:
1110715
Email:
pbelmans@math.uni-bonn.de
Georg Oberdieck
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Email:
georgo@math.uni-bonn.de
Jørgen Vold Rennemo
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway
Email:
jorgeren@uio.no
Received by editor(s):
August 14, 2019
Received by editor(s) in revised form:
December 10, 2019
Published electronically:
June 24, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
