Classification of Hamiltonian S¹-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four

2024/01/27 by Leonor Godinho, Godinho, Leonor, Grace T. Mwakyoma-Oliveira +3
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2401.15466

Abstract

In this paper, we classify Hamiltonian S¹-actions on compact, four dimensional symplectic orbifolds that have isolated singular points with cyclic orbifold structure groups, thus extending the classification due to Karshon to the orbifold setting. To such a space, we associated a combinatorial invariant, a labeled multigraph, that determines the isomorphism type of the space. Moreover, we show that any such space can be obtained by applying finitely many equivariant weighted blow-ups to a minimal space, i.e., one on which no equivariant weighted blow-down can be applied.

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