Hurwitz spaces are spaces of meromorphic functions on algebraic curves. B. Dubrovin introduced Frobenius structures on Hurwitz spaces, which serve as one of the most spectacular examples of such structures. On the other hand, Hurwitz spaces admit natural compactification by stable maps. The main goal of the present paper is to formulate a question concerning the behavior of Dubrovin's Frobenius structures on Hurwitz spaces on the boundary of the compactification. Sample computations justifying the question are given.
Digital Object Identifier: 10.2969/aspm/08310221