Evans–Lekili conjecture on small resolutions of compound Du Val singularities

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Let P∈XP \in X be a compound Du Val singularity, let \Uv\Uv be its Milnor fiber, and let \SHi(\Uv)\SH^i(\Uv) denote its symplectic cohomology in degree ii. Evans–Lekili conjecture. The singularity PP admits a small resolution if and only if dim⁡\SHi(\Uv)\dim \SH^i(\Uv) is constant for every negative cohomological degree. If this holds, that common dimension equals the number of irreducible components of the exceptional locus of a small resolution. The conjecture is proposed in the cited work, and no resolution status is supplied here.

References

Primary source

Yanki Lekili and Kazushi Ueda, “Rabinowitz Fukaya categories as cluster categories”, arXiv:2406.15915 (2026).

Additional references

2 papers in this index state this conjecture (2024). The statement above is taken from the most recent of them; the others are arXiv:2404.17301.

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