Open Access
June 2017 On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32
Maria Donten-Bury, Jarosław A. Wiśniewski
Kyoto J. Math. 57(2): 395-434 (June 2017). DOI: 10.1215/21562261-3821846


We provide a construction of 81 symplectic resolutions of a 4-dimensional quotient singularity obtained by an action of a group of order 32. The existence of such resolutions is known by a result of Bellamy and Schedler. Our explicit construction is obtained via geometric invariant theory (GIT) quotients of the spectrum of a ring graded in the Picard group generated by the divisors associated to the conjugacy classes of symplectic reflections of the group in question. As a result we infer the geometric structure of these resolutions and their flops. Moreover, we represent the group in question as a group of automorphisms of an abelian 4-fold so that the resulting quotient has singularities with symplectic resolutions. This yields a new Kummer-type symplectic 4-fold.


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Maria Donten-Bury. Jarosław A. Wiśniewski. "On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32." Kyoto J. Math. 57 (2) 395 - 434, June 2017.


Received: 24 December 2015; Revised: 17 March 2016; Accepted: 23 March 2016; Published: June 2017
First available in Project Euclid: 9 May 2017

zbMATH: 06736607
MathSciNet: MR3648055
Digital Object Identifier: 10.1215/21562261-3821846

Primary: 14E15
Secondary: 14C20 , 14E30 , 14L24 , 14L30 , 53C26

Keywords: Cox ring , hyper-Kähler manifold , quotient singularity , symplectic resolution

Rights: Copyright © 2017 Kyoto University

Vol.57 • No. 2 • June 2017
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