Stratification of singular hyperkähler quotients (Q2172764)

The author studies hyper-Kähler quotients by non-free group actions, which turn out to be singular, but can be partitioned into smooth hyper-Kähler manifolds. He proves that these partitions are topological stratifications, which can be endowed with Poisson structures to recover the hyper-Kähler structure on the strata. He also proves that these quotients are locally isomorphic to linear complex-symplectic reductions in the GIT sense, [\textit{R. Sjamaar} and \textit{E. Lerman}, Ann. Math. (2) 134, No. 2, 375--422 (1991; Zbl 0759.58019)].