The McKay correspondence for isolated singularities via Floer theory
We prove the generalised McKay correspondence for isolated singularities using Floer theory. Given an isolated singularity Cn/G for a finite subgroup G ⊂ SL(n, C) and any crepant resolution Y , we prove that the rank of positive symplectic cohomology SH∗ +(Y ) is the number |Conj(G)| of conjugacy cl...
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| פורמט: | Journal article |
| שפה: | English |
| יצא לאור: |
International Press
2023
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| סיכום: | We prove the generalised McKay correspondence for isolated singularities using Floer theory. Given an isolated singularity Cn/G for a finite subgroup G ⊂ SL(n, C) and any crepant resolution Y , we prove that the rank of positive symplectic cohomology SH∗ +(Y ) is the number |Conj(G)| of conjugacy classes of G, and that twice the age grading on conjugacy classes is the Z-grading on SH∗−1 + (Y ) by the Conley-Zehnder index. The generalized McKay correspondence follows as SH∗−1 + (Y ) is naturally isomorphic to ordinary cohomology H∗(Y ), due to a vanishing result for full symplectic cohomogy. In the Appendix we construct a novel filtration on the symplectic chain complex for any nonexact convex symplectic manifold, which yields both a Morse-Bott spectral sequence and a construction of positive symplectic cohomology. |
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