Refined curve counting with tropical geometry

@article{Block2015RefinedCC,
  title={Refined curve counting with tropical geometry},
  author={Florian Block and L. Goettsche},
  journal={Compositio Mathematica},
  year={2015},
  volume={152},
  pages={115 - 151}
}
The Severi degree is the degree of the Severi variety parametrizing plane curves of degree $d$ with ${\it\delta}$ nodes. Recently, Göttsche and Shende gave two refinements of Severi degrees, polynomials in a variable $y$, which are conjecturally equal, for large $d$. At $y=1$, one of the refinements, the relative Severi degree, specializes to the (non-relative) Severi degree. We give a tropical description of the refined Severi degrees, in terms of a refined tropical curve count for all toric… Expand
Tropical refined curve counting from higher genera and lambda classes
On refined count of rational tropical curves
Computation of refined toric invariants II
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References

SHOWING 1-10 OF 41 REFERENCES
Universal polynomials for Severi degrees of toric surfaces
A short proof of the Göttsche conjecture
Computing Node Polynomials for Plane Curves
Counting curves on rational surfaces
Labeled floor diagrams for plane curves
A Conjectural Generating Function for Numbers of Curves on Surfaces
...
1
2
3
4
5
...