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arXiv · 1412.4563

The double Gromov-Witten invariants of Hirzebruch surfaces are piecewise polynomial

Federico Ardila·Erwan Brugalle
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Abstract

We define the double Gromov-Witten invariants of Hirzebruch surfaces in analogy with double Hurwitz numbers, and we prove that they satisfy a piecewise polynomiality property analogous to their 1-dimensional counterpart. Furthermore we show that each polynomial piece is either even or odd, and we compute its degree. Our methods combine floor diagrams and Ehrhart theory.

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Federico Ardila, Erwan Brugalle. 2014-12-15. The double Gromov-Witten invariants of Hirzebruch surfaces are piecewise polynomial. https://arxiv.org/abs/1412.4563

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