Abstract
Abstract
Ardila and Block used tropical results of Brugallé and Mikhalkin to
count nodal curves on a certain family of toric surfaces. Building on a
linearity result of the first author, we revisit their
work in the context of the Göttsche–Yau–Zaslow formula for counting nodal
curves on arbitrary smooth surfaces, addressing several
questions they raised by proving stronger versions of their main theorems.
In the process, we give new combinatorial formulas for the coefficients
arising in the Göttsche–Yau–Zaslow formulas, and give correction terms
arising from rational double points in the relevant family of toric surfaces.
Funder
Simons Foundation
National Science Foundation
Subject
Applied Mathematics,General Mathematics
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