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Isolated hypersurface singularities, spectral invariants, and quantum cohomology
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Date
2024Type
- Journal Article
ETH Bibliography
yes
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Abstract
We study the relation between isolated hypersurface singularities (e.g., ADE) and the quantum cohomology ring by using spectral invariants, which are symplectic measurements coming from Floer theory. We prove, under the assumption that the quantum cohomology ring is semi-simple, that (1) if the smooth Fano variety degenerates to a Fano variety with an isolated hypersurface singularity, then the singularity has to be an Aₘ-singularity, (2) if the symplectic manifold contains an Aₘ-configuration of Lagrangian spheres, then there are consequences for the Hofer geometry, and that (3) the Dehn twist reduces spectral invariants. Show more
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publishedExternal links
Journal / series
Journal für die reine und angewandte MathematikPublisher
De GruyterMore
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ETH Bibliography
yes
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