Bi-Lipschitz Invariants in Singularity Theory: Lojasiewicz Exponent and Euler Obstruction
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917432099078144 |
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| author | Araujo, Amanda S. Dalbelo, T. M. da Silva, Thiago |
| author_facet | Araujo, Amanda S. Dalbelo, T. M. da Silva, Thiago |
| contents | In this work, we investigate the bi-Lipschitz invariance of two fundamental local invariants in singularity theory: the Łojasiewicz exponent and the local Euler obstruction. We draw inspiration from Bivià-Ausina and Fukui, whose framework we extend to ideals in rings of analytic functions defined on affine toric varieties. We establish conditions under which these invariants remain unchanged under bi-Lipschitz equivalence. We also provide an answer, to a particular case, to the open question of whether the local Euler obstruction is a bi-Lipschitz invariant. For hypersurfaces with isolated singularities, we show that the Euler obstruction is preserved under non-degeneracy conditions. These results contribute to the understanding of metric invariants in complex analytic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bi-Lipschitz Invariants in Singularity Theory: Lojasiewicz Exponent and Euler Obstruction Araujo, Amanda S. Dalbelo, T. M. da Silva, Thiago Algebraic Geometry 32S15, 32S05, 14M25 In this work, we investigate the bi-Lipschitz invariance of two fundamental local invariants in singularity theory: the Łojasiewicz exponent and the local Euler obstruction. We draw inspiration from Bivià-Ausina and Fukui, whose framework we extend to ideals in rings of analytic functions defined on affine toric varieties. We establish conditions under which these invariants remain unchanged under bi-Lipschitz equivalence. We also provide an answer, to a particular case, to the open question of whether the local Euler obstruction is a bi-Lipschitz invariant. For hypersurfaces with isolated singularities, we show that the Euler obstruction is preserved under non-degeneracy conditions. These results contribute to the understanding of metric invariants in complex analytic geometry. |
| title | Bi-Lipschitz Invariants in Singularity Theory: Lojasiewicz Exponent and Euler Obstruction |
| topic | Algebraic Geometry 32S15, 32S05, 14M25 |
| url | https://arxiv.org/abs/2512.01935 |