On 1-forms on isolated complete intersection curve singularities

Journal of Singularities
volume 18 (2018), 114-118

Received: 6 December 2017. Accepted: 11 March 2018.

DOI: 10.5427/jsing.2018.18h

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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 μ and the Tjurina number τ of any isolated plane curve singularity satisfy the inequality 3μ <4τ

Keywords:

complete intersection, curve singularity, Tjurina number, Milnor number, delta invariant, normalization

Mathematical Subject Classification:

Primary 14H20; Secondary 14F10, 14H50, 32S05

Author(s) information: