A Characterization of Quasi-homogeneous Singularities of Free and Nearly Free Plane Curves
Abstract The goal of this paper is to establish a new characterization of quasi-homogeneous isolated singularities of free curves and nearly free curves $C$ in ${\mathbb{P}}_{\mathbb{C}}^{2}$. The criterion will be in terms of a first syzygy matrix associated with the Jacobian ideal $J_{f}$ of $f$, where $f=0$ is the equation of the plane curve $C$.
Authors
- Rosa M. Miró‐Roig (ORCID: https://orcid.org/0000-0003-1375-6547)
- Aline V. Andrade (ORCID: https://orcid.org/0000-0001-7129-3953)
- Valentina Beorchia (ORCID: https://orcid.org/0000-0003-3681-9045)
Institutions
- Universidade Federal de Minas Gerais (BR)
- University of Trieste (IT)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2024-12-13
- DOI
- https://doi.org/10.1093/imrn/rnae266
- Primary Topic
- Commutative Algebra and Its Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni