Deformation of tropical Hirzebruch surfaces and enumerative geometry

Brugallé, Erwan; Markwig, Hannah

doi:10.1090/jag/671

Authors: Erwan Brugallé and Hannah Markwig
Journal: J. Algebraic Geom. 25 (2016), 633-702
DOI: https://doi.org/10.1090/jag/671
Published electronically: June 2, 2016
MathSciNet review: 3533183
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Abstract | References | Additional Information

Abstract:

We illustrate the use of tropical methods by generalizing a formula due to Abramovich and Bertram, extended later by Vakil. Namely, we exhibit relations between enumerative invariants of the Hirzebruch surfaces $\Sigma _n$ and $\Sigma _{n+2}$, obtained by deforming the first surface to the latter.

Our strategy involves a tropical counterpart of deformations of Hirzebruch surfaces and tropical enumerative geometry on a tropical surface in three-space.

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Additional Information

Erwan Brugallé
Affiliation: Université Pierre et Marie Curie, Paris 6, 4 place Jussieu, 75 005 Paris, France – and – CMLS, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
Email: erwan.brugalle@math.cnrs.fr

Hannah Markwig
Affiliation: Universität des Saarlandes, Fachrichtung Mathematik, Postfach 151150, 66041 Saarbrücken, Germany
Address at time of publication: Eberhard Karls Universität Tübingen, Arbeitsbereich Geometrie, Auf der Morgenstelle 10, 72076 Tübingen, Germany
MR Author ID: 741165
Email: hannah@math.uni-tuebingen.de

Received by editor(s): July 11, 2013
Received by editor(s) in revised form: May 28, 2014
Published electronically: June 2, 2016
Article copyright: © Copyright 2016 University Press, Inc.