A new family of isolated symplectic singularities with trivial local fundamental group
A new family of isolated symplectic singularities with trivial local fundamental group
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DOI：
10.1112/plms.12513
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发表时间：
2021-12
影响因子：
1.8
通讯作者：
G. Bellamy;C'edric Bonnaf'e;Baohua Fu;D. Juteau;Paul D. Levy;E. Sommers
中科院分区：
文献类型：
--
作者：
G. Bellamy;C'edric Bonnaf'e;Baohua Fu;D. Juteau;Paul D. Levy;E. Sommers
我们构造了一个新的具有平凡局部基本群的四维孤立辛奇点无限族，回答了Beauville在2000年提出的一个问题。该族有三种结构：（1）作为C4 $\mathbb {C}^4$与2d $2d $阶二面体群的商的爆破中的奇点，（2）作为与2d $2d $阶二面体群相关联的Calogero-Moser空间在相等参数处的奇点，以及（3）作为sld${\mathfrak {s}}{\mathfrak {l}}_d$中幂零锥的d$d$-重覆盖中的某个Slodowy切片的奇点。
We construct a new infinite family of four‐dimensional isolated symplectic singularities with trivial local fundamental group, answering a question of Beauville raised in 2000. Three constructions are presented for this family: (1) as singularities in blowups of the quotient of C4$\mathbb {C}^4$ by the dihedral group of order 2d$2d$ , (2) as singular points of Calogero–Moser spaces associated with dihedral groups of order 2d$2d$ at equal parameters, and (3) as singularities of a certain Slodowy slice in the d$d$ ‐fold cover of the nilpotent cone in sld${\mathfrak {s}}{\mathfrak {l}}_d$ .