Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866913699713777664 |
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| author | Biswas, Indranil Mukherjee, Ritwik Thakre, Varun |
| author_facet | Biswas, Indranil Mukherjee, Ritwik Thakre, Varun |
| contents | We obtain a formula for the number of genus two curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This is done by extending the symplectic approach of Aleksey Zinger. This enumerative problem is expressed as the difference between the symplectic invariant and an intersection number on the moduli space of rational curves on the surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1511_04900 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure Biswas, Indranil Mukherjee, Ritwik Thakre, Varun Algebraic Geometry Symplectic Geometry 53D45, 14N35, 14J45 We obtain a formula for the number of genus two curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This is done by extending the symplectic approach of Aleksey Zinger. This enumerative problem is expressed as the difference between the symplectic invariant and an intersection number on the moduli space of rational curves on the surface. |
| title | Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure |
| topic | Algebraic Geometry Symplectic Geometry 53D45, 14N35, 14J45 |
| url | https://arxiv.org/abs/1511.04900 |