A note on planarity stratification of hurwitz spaces
Abstract
Abstract.
One can easily show that any meromorphic function on a comple
x
closed Riemann surface can be represented as a composition o
f a birational
map of this surface to
CP
2
and a projection of the image curve from an ap-
propriate point
p
∈
CP
2
to the pencil of lines through
p
. We introduce a
natural stratification of Hurwitz spaces according to the mi
nimal degree of a
plane curve such that a given meromorphic function can be rep
resented in the
above way and calculate the dimensions of these strata. We ob
serve that they
are closely related to a family of Severi varieties studied e
arlier by J. Harris,
Z. Ran and I. Tyomkin
Citation
Ongaro J, Shapiro B. (2014).Planarity stratification of Hurwitz spaces. pp.1-12Publisher
University of Nairobi