Year: 2025
Type: article
Abstract: 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.
Source: Algebraic Combinatorics
DOI: 10.5802/alco.444
Author: Gurvan Mével
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415736001