2018/07/16 by Maxence Mayrand, Mayrand, Maxence
Mathematics · #32M05 #53C26 #53D20 #57N80 #58A35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1807.05992
openalex publication_date 2018/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hyperkahler quotients by non-free actions are typically highly singular, but are remarkably still partitioned into smooth hyperkahler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow the quotients with global Poisson structures which induce the hyperkahler structures on the strata. Finally, we give a local model which shows that these quotients are locally isomorphic to linear complex-symplectic reductions in the GIT sense. These results can be thought of as the hyperkahler analogues of Sjamaar-Lerman's theorems for symplectic reduction. They are based on a local normal form for the underlying complex-Hamiltonian manifold, which may be of independent interest.