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Severi degrees on toric surfaces

Severi degrees on toric surfaces 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal für die reine und angewandte Mathematik de Gruyter

Severi degrees on toric surfaces

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1435-5345
eISSN
1435-5345
DOI
10.1515/crelle-2015-0059
Publisher site
See Article on Publisher Site

Abstract

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

Journal für die reine und angewandte Mathematikde Gruyter

Published: Jun 1, 2018

References