Higher genus reduced Gromov--Witten invariants via desingularizations of sheaves
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866915913782001664 |
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| author | Rabano, Alberto Cobos Mann, Etienne Manolache, Cristina Picciotto, Renata |
| author_facet | Rabano, Alberto Cobos Mann, Etienne Manolache, Cristina Picciotto, Renata |
| contents | Given $\mathfrak{F}$ a coherent sheaf on a Noetherian integral algebraic stack $\mathfrak{P}$, we give two constructions of stacks $\widetilde{\mathfrak{P}}$, equipped with birational morphisms $p:\widetilde{\mathfrak{P}}\to \mathfrak{P}$ such that $p^*\mathfrak{F}$ is simpler: in the Rossi construction, the torsion free part of $p^*\mathfrak{F}$ is locally free; in the Hu--Li diagonalization construction, $p^*\mathfrak{F}$ is a union of locally free sheaves. We use these constructions to define reduced Gromov--Witten invariants of a large class of GIT quotients in all genera. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher genus reduced Gromov--Witten invariants via desingularizations of sheaves Rabano, Alberto Cobos Mann, Etienne Manolache, Cristina Picciotto, Renata Algebraic Geometry 14N35 (Primary) 14A20 (Secondary) Given $\mathfrak{F}$ a coherent sheaf on a Noetherian integral algebraic stack $\mathfrak{P}$, we give two constructions of stacks $\widetilde{\mathfrak{P}}$, equipped with birational morphisms $p:\widetilde{\mathfrak{P}}\to \mathfrak{P}$ such that $p^*\mathfrak{F}$ is simpler: in the Rossi construction, the torsion free part of $p^*\mathfrak{F}$ is locally free; in the Hu--Li diagonalization construction, $p^*\mathfrak{F}$ is a union of locally free sheaves. We use these constructions to define reduced Gromov--Witten invariants of a large class of GIT quotients in all genera. |
| title | Higher genus reduced Gromov--Witten invariants via desingularizations of sheaves |
| topic | Algebraic Geometry 14N35 (Primary) 14A20 (Secondary) |
| url | https://arxiv.org/abs/2310.06727 |