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April 2009 The Hilbert scheme of points for supersingular abelian surfaces
Stefan Schröer
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Ark. Mat. 47(1): 143-181 (April 2009). DOI: 10.1007/s11512-007-0065-6


We study the geometry of Hilbert schemes of points on abelian surfaces and Beauville’s generalized Kummer varieties in positive characteristics. The main result is that, in characteristic two, the addition map from the Hilbert scheme of two points to the abelian surface is a quasifibration such that all fibers are nonsmooth. In particular, the corresponding generalized Kummer surface is nonsmooth, and minimally elliptic singularities occur in the supersingular case. We unravel the structure of the singularities in dependence of p-rank and a-number of the abelian surface. To do so, we establish a McKay Correspondence for Artin’s wild involutions on surfaces. Along the line, we find examples of canonical singularities that are not rational singularities.


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Stefan Schröer. "The Hilbert scheme of points for supersingular abelian surfaces." Ark. Mat. 47 (1) 143 - 181, April 2009.


Received: 19 February 2007; Revised: 8 August 2007; Published: April 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1190.14032
MathSciNet: MR2480919
Digital Object Identifier: 10.1007/s11512-007-0065-6

Rights: 2008 © Institut Mittag-Leffler


Vol.47 • No. 1 • April 2009
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