A note on planarity stratication of Hurwitz spaces
2015 (English)In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 58, no 3, 596-609 p.Article in journal (Refereed) Published
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 from an appropriate point $p\in \CP^2$ 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.
Place, publisher, year, edition, pages
2015. Vol. 58, no 3, 596-609 p.
Hurwitz spaces, plane curves
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-126347OAI: oai:DiVA.org:su-126347DiVA: diva2:899230