Quantum cohomology and Floer invariants of semiprojective toric manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929677031964672 |
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| author | Ritter, Alexander F. Živanović, Filip |
| author_facet | Ritter, Alexander F. Živanović, Filip |
| contents | We use Floer theory to describe invariants of symplectic $\mathbb{C}^*$-manifolds admitting several commuting $\mathbb{C}^*$-actions. The $\mathbb{C}^*$-actions induce filtrations by ideals on quantum cohomology, as well as filtrations on Hamiltonian Floer cohomologies, and we prove relationships between these filtrations. We also carry this out in the equivariant setting, in particular $\mathbb{C}^*$-actions then give rise to Hilbert-Poincaré polynomials on ordinary cohomology that depend on Floer theory. For semiprojective toric manifolds, we obtain an explicit presentation for quantum and symplectic cohomology in the Fano and CY setting, both in the equivariant and non-equivariant setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum cohomology and Floer invariants of semiprojective toric manifolds Ritter, Alexander F. Živanović, Filip Symplectic Geometry Algebraic Geometry 53D40, 53D45, 53D05 14M25 (primary) 14N35 (secondary) We use Floer theory to describe invariants of symplectic $\mathbb{C}^*$-manifolds admitting several commuting $\mathbb{C}^*$-actions. The $\mathbb{C}^*$-actions induce filtrations by ideals on quantum cohomology, as well as filtrations on Hamiltonian Floer cohomologies, and we prove relationships between these filtrations. We also carry this out in the equivariant setting, in particular $\mathbb{C}^*$-actions then give rise to Hilbert-Poincaré polynomials on ordinary cohomology that depend on Floer theory. For semiprojective toric manifolds, we obtain an explicit presentation for quantum and symplectic cohomology in the Fano and CY setting, both in the equivariant and non-equivariant setting. |
| title | Quantum cohomology and Floer invariants of semiprojective toric manifolds |
| topic | Symplectic Geometry Algebraic Geometry 53D40, 53D45, 53D05 14M25 (primary) 14N35 (secondary) |
| url | https://arxiv.org/abs/2501.09011 |