1 results
Equisingularity in pencils of curves on germs of reduced complex surfaces
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 3 / August 2024
- Published online by Cambridge University Press:
- 04 June 2024, pp. 990-1012
-
- Article
-
- You have access
- HTML
- Export citation
-
We study pencils of curves on a germ of complex reduced surface
$(S,0)$. These are families of curves parametrized by 
$ \mathbb{P}^1 $ having 0 as the unique common point. We prove that for 
$w\in \mathbb{P}^1$, the corresponding curve of the pencil does not have the generic topology if and only if either the corresponding curve of the pulled-back pencil to the normalized surface has a non generic topology or w is a limit value for the function 
$ f/g $ along the singular locus of 
$(S,0)$, where f and g are generators of the pencil.
