A short proof of the multiple cover formula for point insertions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908761906479104 |
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| author | Blomme, Thomas |
| author_facet | Blomme, Thomas |
| contents | A few years ago, G. Oberdieck conjectured a multiple cover fomula that determines the number of curves of fixed genus and degree passing through a configuration of points in an abelian surface. This formula was proved by the author using tropical techniques and Nishinou's correspondence theorem. Using the same techniques, we give a much shorter proof of the multiple cover formula for point insertions, relying on the same geometrical idea, but avoiding any kind of tropical enumeration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A short proof of the multiple cover formula for point insertions Blomme, Thomas Algebraic Geometry Primary 14N10, 14T90, 14K12, Secondary 14N35 A few years ago, G. Oberdieck conjectured a multiple cover fomula that determines the number of curves of fixed genus and degree passing through a configuration of points in an abelian surface. This formula was proved by the author using tropical techniques and Nishinou's correspondence theorem. Using the same techniques, we give a much shorter proof of the multiple cover formula for point insertions, relying on the same geometrical idea, but avoiding any kind of tropical enumeration. |
| title | A short proof of the multiple cover formula for point insertions |
| topic | Algebraic Geometry Primary 14N10, 14T90, 14K12, Secondary 14N35 |
| url | https://arxiv.org/abs/2501.01274 |