Kirwan surjectivity and Lefschetz–Sommese theorems for a generalized hyperkähler reduction

Let G be a compact Lie group. We study a class of Hamiltonian ( G × S 1 ) -manifolds decorated with a function s with certain equivariance properties, under conditions on the G -action which we call of (semi-)linear type . In this context, a close analogue of hyperkähler reduction is defined, and ou...

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Bibliographic Details
Published in:Geometriae dedicata 2023-10, Vol.217 (5), Article 94
Main Authors: Fisher, Jonathan, Jeffrey, Lisa, Malusà, Alessandro, Rayan, Steven
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hamiltonian functions
Hyperbolic Geometry
Lie groups
Manifolds
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Reduction
Topology
Toruses
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Summary:Let G be a compact Lie group. We study a class of Hamiltonian ( G × S 1 ) -manifolds decorated with a function s with certain equivariance properties, under conditions on the G -action which we call of (semi-)linear type . In this context, a close analogue of hyperkähler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan’s map. As a particular case, our setting includes a class of hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-023-00831-w