Free divisors in a pencil of curves
Algebraic Geometry
2016-01-13 v2 Algebraic Topology
Abstract
A plane curve on a the projective space over a field of characteristic zero is free if its associated sheaf T of tangent vector fields tangent is a free module. Relatively few free curves are known. Here we prove that a divisor consisting of a union of curves of a pencil of plane projective curves with the same degree and with a smooth base locus is a free divisor if and only this union contains all the singular members of the pencil and its Jacobian ideal is locally a complete intersection.
Keywords
Cite
@article{arxiv.1502.02416,
title = {Free divisors in a pencil of curves},
author = {Jean Vallès},
journal= {arXiv preprint arXiv:1502.02416},
year = {2016}
}