Combinatorial G\"ottsche-Schroeter invariants in any genus
Algebraic Geometry
2024-11-05 v1 Combinatorics
Abstract
G\"ottsche-Schroeter invariants are a genus 0 extension of Block-G\"ottsche 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 G\"ottsche-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.
Cite
@article{arxiv.2411.02312,
title = {Combinatorial G\"ottsche-Schroeter invariants in any genus},
author = {Gurvan Mével},
journal= {arXiv preprint arXiv:2411.02312},
year = {2024}
}