A Note on Planarity Stratification of Hurwitz Spaces

Ongaro, Jared ; Shapiro, Boris

Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 596-609

Résumé

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.

Détail

DOI : 10.4153/CMB-2015-015-x

Mots-clés : 14H50, 14H05, Hurwitz spaces, meromorphic functions, Severi varieties

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