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arXiv · 2609.26948

Open extension of a genus zero Hurwitz-Frobenius manifold

Alexey Basalaev·Anton Rarovskii
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Abstract

Every Dubrovin--Frobenius manifold provides a solution to the WDVV equation, that was initially formulated in the study of the moduli space of curves. During the last two decades special attention was given to the "open" version of the moduli space of curves. Its genus zero intersection theory is governed by the system of equations called open WDVV equation, that extends "classical" WDVV equation. In this note we study Dubrovin--Frobenius manifold structures on the Hurwitz spaces of genus zero. We construct explicitly the solutions to open WDVV equation for these Dubrovin--Frobenius manifolds and show that these solutions appear as the restriction of the Dubrovin--Frobenius structure to its discriminant.

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Alexey Basalaev, Anton Rarovskii. 2026-09-22. Open extension of a genus zero Hurwitz-Frobenius manifold. https://arxiv.org/abs/2609.26948

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