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BY 4.0 license Open Access Published by De Gruyter Open Access September 2, 2022

Stratification of singular hyperkähler quotients

  • Maxence Mayrand EMAIL logo
From the journal Complex Manifolds

Abstract

Hyperkähler quotients by non-free actions are typically singular, but are nevertheless partitioned into smooth hyperkähler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow the quotients with global Poisson structures which recover the hyperkähler 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 hyperkähler analogues of Sjamaar–Lerman’s theorems for singular symplectic reduction. They are based on a local normal form for the underlying complex-Hamiltonian manifold, which may be of independent interest.

MSC 2010: 53C26; 53D20; 57N80; 58A35; 32M05

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Received: 2022-01-07
Accepted: 2022-08-17
Published Online: 2022-09-02

© 2022 Maxence Mayrand, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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