Fixed-domain curve counts for blow-ups of projective space
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911496620998656 |
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| author | Cela, Alessio Lian, Carl |
| author_facet | Cela, Alessio Lian, Carl |
| contents | We study the problem of counting pointed curves of fixed complex structure in blow-ups of projective space at general points. The geometric and virtual (Gromov-Witten) counts are found to agree asymptotically in the Fano (and some $(-K)$-nef) examples, but not in general. For toric blow-ups, geometric counts are expressed in terms of integrals on products of Jacobians and symmetric products of the domain curves, and evaluated explicitly in genus 0 and in the case of $\text{Bl}_q(\mathbb{P}^r)$. Virtual counts for $\text{Bl}_q(\mathbb{P}^r)$ are also computed via the quantum cohomology ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03433 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fixed-domain curve counts for blow-ups of projective space Cela, Alessio Lian, Carl Algebraic Geometry We study the problem of counting pointed curves of fixed complex structure in blow-ups of projective space at general points. The geometric and virtual (Gromov-Witten) counts are found to agree asymptotically in the Fano (and some $(-K)$-nef) examples, but not in general. For toric blow-ups, geometric counts are expressed in terms of integrals on products of Jacobians and symmetric products of the domain curves, and evaluated explicitly in genus 0 and in the case of $\text{Bl}_q(\mathbb{P}^r)$. Virtual counts for $\text{Bl}_q(\mathbb{P}^r)$ are also computed via the quantum cohomology ring. |
| title | Fixed-domain curve counts for blow-ups of projective space |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2303.03433 |