PreprintCC BY 4.0arXiv
Open extension of a genus zero Hurwitz-Frobenius manifold
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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BibTeX
@misc{basalaev2026open,
title = {{Open extension of a genus zero Hurwitz-Frobenius manifold}},
author = {Alexey Basalaev and Anton Rarovskii},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.26948},
eprint = {2609.26948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26948},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Open extension of a genus zero Hurwitz-Frobenius manifold
AU - Alexey Basalaev
AU - Anton Rarovskii
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.26948
UR - https://arxiv.org/abs/2609.26948
AB - 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.
ER -