English

Characterizing normal crossing hypersurfaces

Algebraic Geometry 2018-05-04 v2 Complex Variables

Abstract

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito's theory of free divisors, also a characterization in terms of logarithmic differential forms and vector fields is found and and finally another one in terms of the logarithmic residue using recent results of M. Granger and M. Schulze.

Keywords

Cite

@article{arxiv.1201.6276,
  title  = {Characterizing normal crossing hypersurfaces},
  author = {Eleonore Faber},
  journal= {arXiv preprint arXiv:1201.6276},
  year   = {2018}
}

Comments

v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2 figures

R2 v1 2026-06-21T20:11:55.722Z