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Combinatorial Göttsche-Schroeter invariants in any genus
Mével, Gurvan1
1 Université de Genève Section de Mathématiques rue du Conseil-Général 7-9 1205 Genève (Suisse)
Algebraic Combinatorics, Volume 8 (2025) no. 5, pp. 1353-1386

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-Schroeter 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.444
Classification: 14T15, 14T90, 05E14, 14N10
Keywords: tropical refined invariants, floor diagrams, Göttsche-Schroeter invariants

Mével, Gurvan 1

1 Université de Genève Section de Mathématiques rue du Conseil-Général 7-9 1205 Genève (Suisse)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Mével, Gurvan. Combinatorial Göttsche-Schroeter invariants in any genus. Algebraic Combinatorics, Volume 8 (2025) no. 5, pp. 1353-1386. doi: 10.5802/alco.444

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