Combinatorial Göttsche-Schroeter invariants in any genus
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
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| _version_ | 1866912104804515840 |
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| author | Mével, Gurvan |
| author_facet | Mével, Gurvan |
| contents | Göttsche-Schroeter invariants are a genus 0 extension of Block-Göttsche invariants. They interpolate between Welschinger invariants involving pairs of complex conjugated points and genus 0 descendant Gromov-Witten invariants. They can be computed by a floor diagram algorithm.
In this paper, we show that this floor diagrams recipe actually leads to some invariants in any genus. This generalizes Göttsche-Schroter invariant in higher genus in a combinatorial way. We then prove some polynomiality result and establish a link with invariants defined by Shustin and Sinichkin. We provide many examples. In particular, we conjecture that these combinatorial invariants satisfy the Abramovich-Bertram formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial Göttsche-Schroeter invariants in any genus Mével, Gurvan Algebraic Geometry Combinatorics Göttsche-Schroeter invariants are a genus 0 extension of Block-Göttsche invariants. They interpolate between Welschinger invariants involving pairs of complex conjugated points and genus 0 descendant Gromov-Witten invariants. They can be computed by a floor diagram algorithm. In this paper, we show that this floor diagrams recipe actually leads to some invariants in any genus. This generalizes Göttsche-Schroter invariant in higher genus in a combinatorial way. We then prove some polynomiality result and establish a link with invariants defined by Shustin and Sinichkin. We provide many examples. In particular, we conjecture that these combinatorial invariants satisfy the Abramovich-Bertram formula. |
| title | Combinatorial Göttsche-Schroeter invariants in any genus |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2411.02312 |