Resolution of four-dimensional symplectic orbifolds. (English) Zbl 1476.57029
Using techniques from complex geometry and the gluing of symplectic forms, the authors give a method to resolve four-dimensional symplectic orbifolds. Their main result is: Let \((X,\omega)\) be a compact symplectic 4-orbifold. There exists a symplectic manifold \((\tilde{X},\tilde{\omega})\) and a smooth map \(\pi: (\tilde{X},\tilde{\omega})\to (X,\omega)\) which is a symplectomorphism outside an arbitrarily small neighborhood of the isotropy set of \(X\). The first section of the paper outlines the history of the problem and the last section gives some explicit examples.
Reviewer: Joseph E. Borzellino (San Luis Obispo)
MSC:
| 57K43 | Symplectic structures in 4 dimensions |
| 57R18 | Topology and geometry of orbifolds |
| 53D35 | Global theory of symplectic and contact manifolds |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
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