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- Title
Isolated hypersurface singularities, spectral invariants, and quantum cohomology.
- Authors
Kawamoto, Yusuke
- 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 A m -singularity, (2) if the symplectic manifold contains an A m -configuration of Lagrangian spheres, then there are consequences for the Hofer geometry, and that (3) the Dehn twist reduces spectral invariants.
- Subjects
QUANTUM rings; SYMPLECTIC manifolds; HYPERSURFACES
- Publication
Journal für die Reine und Angewandte Mathematik, 2024, Vol 2024, Issue 811, p183
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2024-0013