Properties of Gromov-Witten invariants defined via global Kuranishi charts
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915829144092672 |
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| author | Hirschi, Amanda |
| author_facet | Hirschi, Amanda |
| contents | Using the global Kuranishi charts constructed in \cite{HS22}, we define gravitational descendants and equivariant Gromov-Witten invariants for general symplectic manifolds. We prove that that these invariants, equivariant and non-equivariant, satisfy the axioms of Kontsevich and Manin and their generalisations. A virtual localisation formula holds in this setting; we use it derive an explicit formula for the equivariant GW invariants of a class of Hamiltonian manifolds. A comparison with the GW invariants of \cite{RT97} is given in the semipositive case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03625 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Properties of Gromov-Witten invariants defined via global Kuranishi charts Hirschi, Amanda Symplectic Geometry 53D45 Using the global Kuranishi charts constructed in \cite{HS22}, we define gravitational descendants and equivariant Gromov-Witten invariants for general symplectic manifolds. We prove that that these invariants, equivariant and non-equivariant, satisfy the axioms of Kontsevich and Manin and their generalisations. A virtual localisation formula holds in this setting; we use it derive an explicit formula for the equivariant GW invariants of a class of Hamiltonian manifolds. A comparison with the GW invariants of \cite{RT97} is given in the semipositive case. |
| title | Properties of Gromov-Witten invariants defined via global Kuranishi charts |
| topic | Symplectic Geometry 53D45 |
| url | https://arxiv.org/abs/2312.03625 |