Refined curve counting with tropical geometry

  title={Refined curve counting with tropical geometry},
  author={Florian Block and Lothar Goettsche},
  journal={Compositio Mathematica},
  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
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