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Mathematics > Symplectic Geometry
Title: Isolated hypersurface singularities, spectral invariants, and quantum cohomology
(Submitted on 4 Apr 2023 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We study the relation between isolated hypersurface singularities (e.g. ADE) and the quantum cohomology ring by using spectral invariants, which are symplectic invariants coming from Floer theory. We prove, under the assumption that the quantum cohomology ring is semi-simple, that (1) if the smooth Fano variety (or the symplectic manifold) degenerates to a Fano variety with an isolated hypersurface singularity, then the singularity has to be an $A_m$-singularity, (2) if the symplectic manifold contains an $A_m$-configuration of Lagrangian spheres, then there are consequences on the Hofer geometry, and that (3) the Dehn twist reduces spectral invariants.
Submission history
From: Yusuke Kawamoto [view email][v1] Tue, 4 Apr 2023 14:57:32 GMT (37kb)
[v2] Wed, 27 Mar 2024 09:28:28 GMT (35kb)
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