Gromov-Witten invariants in family and quantum cohomology
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908398084161536 |
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| author | Biswas, Indranil Das, Nilkantha Oh, Jeongseok Paul, Anantadulal |
| author_facet | Biswas, Indranil Das, Nilkantha Oh, Jeongseok Paul, Anantadulal |
| contents | A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r general lines while passing through given s general points, where r + 2s = 3d + 2, firstly proved by R. Mukherjee, R. Kumar Singh and the fourth named author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06616 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gromov-Witten invariants in family and quantum cohomology Biswas, Indranil Das, Nilkantha Oh, Jeongseok Paul, Anantadulal Algebraic Geometry 14N35 A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r general lines while passing through given s general points, where r + 2s = 3d + 2, firstly proved by R. Mukherjee, R. Kumar Singh and the fourth named author. |
| title | Gromov-Witten invariants in family and quantum cohomology |
| topic | Algebraic Geometry 14N35 |
| url | https://arxiv.org/abs/2408.06616 |