On 1-forms on isolated complete intersection curve singularities

Alexandru Dimca; Gert-Martin Greuel

On 1-forms on isolated complete intersection curve singularities

Algebraic Geometry 2019-09-17 v2 Commutative Algebra Complex Variables

Authors: Alexandru Dimca , Gert-Martin Greuel

Abstract

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity. They are used to study the pull-back of holomorphic 1-forms on an isolated complete intersection curve singularity under the normalization morphism. We wonder whether the Milnor number $\mu$ and the Tjurina number $\tau$ of any isolated plane curve singularity satisfy the inequality $3\mu <4\tau$ .

Keywords

singularity theory curves algebraic curves

Cite

@article{arxiv.1709.01451,
  title  = {On 1-forms on isolated complete intersection curve singularities},
  author = {Alexandru Dimca and Gert-Martin Greuel},
  journal= {arXiv preprint arXiv:1709.01451},
  year   = {2019}
}

Comments

This preprint supersedes the preprint arXiv: 1708.09731 by A. Dimca and the preprint arXiv: 1709.00679 by G.-M. Greuel. version 2: minor changes

On 1-forms on isolated complete intersection curve singularities

Abstract

Keywords

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