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Article Dans Une Revue Journal of Algebraic Geometry Année : 2016

Deformation of tropical Hirzebruch surfaces and enumerative geometry

Résumé

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.

Dates et versions

hal-02175128 , version 1 (05-07-2019)

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Erwan Brugallé, Hannah Markwig. Deformation of tropical Hirzebruch surfaces and enumerative geometry. Journal of Algebraic Geometry, 2016, 25 (4), pp.633-702. ⟨10.1090/jag/671⟩. ⟨hal-02175128⟩
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