Abstract:Take a closed monotone symplectic manifold containing a smooth anticanonical divisor. The quantum connection on its cohomology has singularities at zero and infinity (in the quantum parameter). At zero it has a regular singular point, by definition. We show that the singularity at infinity is of unramified exponential type. The argument involves: realizing cohomology as a deformation of the symplectic cohomology of the divisor complement; the corresponding deformation of the wrapped Fukaya category; a new categorical interpretation of the Fourier-Laplace transform of D-modules; and the regularity theorem of Petrov-Vaintrob-Vologodsky in noncommutative geometry.
From: Paul Seidel [view email]
[v1]
Fri, 25 Aug 2023 01:44:54 UTC (1,276 KB)
[v2]
Fri, 16 Aug 2024 22:42:38 UTC (1,278 KB)
[v3]
Fri, 23 Aug 2024 19:36:23 UTC (1,278 KB)
[v4]
Wed, 17 Jun 2026 18:33:33 UTC (1,295 KB)
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