English

The Bruce-Roberts Tjurina number of holomorphic 1-forms along complex analytic varieties

Complex Variables 2024-10-01 v1 Algebraic Geometry

Abstract

We introduce the notion of the Bruce-Roberts Tjurina number for holomorphic 1-forms relative to a pair (X,V)(X,V) of complex analytic subvarieties. When the pair (X,V)(X,V) consists of isolated complex analytic hypersurfaces, we prove that the Bruce-Roberts Tjurina number is related to the Bruce-Roberts number, the Tjurina number of the 1-form with respect to VV and the Tjurina number of XX, among other invariants. As an application, we present a quasihomogeneity result for germs of holomorphic foliations in complex dimension two.

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Cite

@article{arxiv.2409.19814,
  title  = {The Bruce-Roberts Tjurina number of holomorphic 1-forms along complex analytic varieties},
  author = {Pedro Barbosa and Arturo Fernández-Pérez and Víctor León},
  journal= {arXiv preprint arXiv:2409.19814},
  year   = {2024}
}

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15 pages