English

Adjoint divisors and free divisors

Algebraic Geometry 2014-09-22 v4

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.

Keywords

Cite

@article{arxiv.1001.1095,
  title  = {Adjoint divisors and free divisors},
  author = {David Mond and Mathias Schulze},
  journal= {arXiv preprint arXiv:1001.1095},
  year   = {2014}
}

Comments

24 pages, 1 figure

R2 v1 2026-06-21T14:31:59.706Z