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arXiv · 2401.15466

Classification of Hamiltonian $S^1$-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four

Leonor Godinho·Grace T. Mwakyoma-Oliveira·Daniele Sepe
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Abstract

In this paper, we classify Hamiltonian $S^1$-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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Leonor Godinho, Grace T. Mwakyoma-Oliveira, Daniele Sepe. 2024-01-27. Classification of Hamiltonian $S^1$-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four. https://arxiv.org/abs/2401.15466

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