Published online by Cambridge University Press: 20 November 2018
One can easily show that any meromorphic function on a complex closed Riemann surface can be represented as a composition of a birational map of this surface to $\mathbb{C}{{\mathbb{P}}^{2}}$ and a projection of the image curve froman appropriate point $p\in \mathbb{C}{{\mathbb{P}}^{2}}$ to the pencil of lines through $p$ . We introduce a natural stratification of Hurwitz spaces according to the minimal degree of a plane curve such that a given meromorphic function can be represented in the above way and calculate the dimensions of these strata. We observe that they are closely related to a family of Severi varieties studied earlier by J. Harris, Z. Ran, and I. Tyomkin.