2015/02/20 by Jared Ongaro, Boris Shapiro
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications
paper · pdf · doi:10.4153/cmb-2015-015-x
Abstract 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 ℂℙ 2 and a projection of the image curve froman appropriate point p ∊ ℂℙ 2 to the pencil of lines through p . We introduce a natural stratiûcation 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.