AbstractArdila and Block used tropical results of Brugallé and Mikhalkin tocount nodal curves on a certain family of toric surfaces. Building on alinearity result of the first author, we revisit theirwork in the context of the Göttsche–Yau–Zaslow formula for counting nodalcurves on arbitrary smooth surfaces, addressing severalquestions they raised by proving stronger versions of their main theorems.In the process, we give new combinatorial formulas for the coefficientsarising in the Göttsche–Yau–Zaslow formulas, and give correction termsarising from rational double points in the relevant family of toric surfaces.
Journal für die reine und angewandte Mathematik – de Gruyter
Published: Jun 1, 2018
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