A Note on Planarity Stratification of Hurwitz Spaces
Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 596-609
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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.
Mots-clés :
14H50, 14H05, Hurwitz spaces, meromorphic functions, Severi varieties
Ongaro, Jared; Shapiro, Boris. A Note on Planarity Stratification of Hurwitz Spaces. Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 596-609. doi: 10.4153/CMB-2015-015-x
@article{10_4153_CMB_2015_015_x,
author = {Ongaro, Jared and Shapiro, Boris},
title = {A {Note} on {Planarity} {Stratification} of {Hurwitz} {Spaces}},
journal = {Canadian mathematical bulletin},
pages = {596--609},
year = {2015},
volume = {58},
number = {3},
doi = {10.4153/CMB-2015-015-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-015-x/}
}
TY - JOUR AU - Ongaro, Jared AU - Shapiro, Boris TI - A Note on Planarity Stratification of Hurwitz Spaces JO - Canadian mathematical bulletin PY - 2015 SP - 596 EP - 609 VL - 58 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-015-x/ DO - 10.4153/CMB-2015-015-x ID - 10_4153_CMB_2015_015_x ER -
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