Pencils and critical locus on normal surfaces
Algebraic Geometry
2016-01-08 v1
Abstract
We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Then we show that the critical locus associated to the pencil is linked to the special elements. This gives a decomposition of the critical locus through the minimal good resolution and as a consequence, information on the topological type of the critical locus.
Cite
@article{arxiv.1601.01647,
title = {Pencils and critical locus on normal surfaces},
author = {F. Delgado and H. Maugendre},
journal= {arXiv preprint arXiv:1601.01647},
year = {2016}
}