pith. sign in

arxiv: 1001.1095 · v4 · pith:4O26J6N6new · submitted 2010-01-07 · 🧮 math.AG

Adjoint divisors and free divisors

classification 🧮 math.AG
keywords freedivisordivisorsadjointcomplexfirstaddingalready
0
0 comments X
read the original abstract

We describe two situations where adding the adjoint divisor to a divisor D with smooth normalization yields a free divisor. Both also involve stability or versality. In the first, D is the image of a corank one stable germ of a map from complex n-space to complex (n+1)-space, and is not free. In the second, D is the discriminant of a versal deformation of a weighted homogeneous function with isolated critical point (subject to certain numerical conditions on the weights). Here D itself is already free. We also prove an elementary result, inspired by these first two, from which we obtain a plethora of new examples of free divisors. The presented results seem to scratch the surface of a more general phenomenon that is still to be revealed.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.