Tropical curves in abelian surfaces III: pearl diagrams and multiple cover formulas
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910383435939840 |
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| author | Blomme, Thomas |
| author_facet | Blomme, Thomas |
| contents | This paper is the third installment in a series of papers devoted to the computation of enumerative invariants of abelian surfaces through the tropical approach. We develop a pearl diagram algorithm similar to the floor diagram algorithm used in toric surfaces that concretely solves the tropical problem.
These diagrams can be used to prove specific cases of Oberdieck's multiple cover formula that reduce the computation of invariants for non-primitive classes to the primitive case, getting rid of all diagram considerations and providing short explicit formulas. The latter can be used to prove the quasi-modularity of generating series of classical invariants, and the polynomiality of coefficients of fixed codegree in the refined invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07684 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tropical curves in abelian surfaces III: pearl diagrams and multiple cover formulas Blomme, Thomas Algebraic Geometry Combinatorics 14N10, 14T90, 11G10, 14K05, 14H99 This paper is the third installment in a series of papers devoted to the computation of enumerative invariants of abelian surfaces through the tropical approach. We develop a pearl diagram algorithm similar to the floor diagram algorithm used in toric surfaces that concretely solves the tropical problem. These diagrams can be used to prove specific cases of Oberdieck's multiple cover formula that reduce the computation of invariants for non-primitive classes to the primitive case, getting rid of all diagram considerations and providing short explicit formulas. The latter can be used to prove the quasi-modularity of generating series of classical invariants, and the polynomiality of coefficients of fixed codegree in the refined invariants. |
| title | Tropical curves in abelian surfaces III: pearl diagrams and multiple cover formulas |
| topic | Algebraic Geometry Combinatorics 14N10, 14T90, 11G10, 14K05, 14H99 |
| url | https://arxiv.org/abs/2205.07684 |