Refined count for rational tropical curves in arbitrary dimension
Thomas Blomme
TL;DR
This paper introduces a generalized refined multiplicity for rational tropical curves in any dimension, proving invariance in enumerative problems and defining Block-G"ottsche polynomials beyond two dimensions.
Contribution
It extends the refined multiplicity concept to arbitrary dimensions and establishes invariance results for rational tropical curve counts.
Findings
Invariance of rational tropical curve counts with the new refined multiplicity
Definition of Block-G"ottsche polynomials in any dimension
Generalization of previous two-dimensional results
Abstract
In this paper we introduce a refined multiplicity for rational tropical curves in arbitrary dimension, which generalizes the refined multiplicity introduced by F. Block and L. G\"ottsche in arXiv:1407.2901 . We then prove an invariance statement for the count of rational tropical curves in several enumerative problems using this new refined multiplicity. This leads to the definition of Block-G\"ottsche polynomials in any dimension.
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