Disentangling mappings defined on ICIS
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909154546810880 |
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| author | Fernández-Hernández, Alberto |
| author_facet | Fernández-Hernández, Alberto |
| contents | Let $(X,S)$ be an isolated complete intersection singularity of dimension $n$, and let $f:(X,S)\rightarrow (\mathbb{C}^{n+1},0)$ be a germ of $\mathscr{A}$-finite mapping. In this master's degree final project, our main contribution is that we show the case $n=2$ of the general Mond conjecture, which states that $μ_I(X,f)\geq \text{codim}_{\mathscr{A}_e}(X,f)$, with equality provided $(X,f)$ is weighted homogeneous. Before this project, the only known case for which the conjecture was known to hold is in the case that $n=1$ and $(X,S)$ is a plane curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Disentangling mappings defined on ICIS Fernández-Hernández, Alberto Algebraic Geometry Primary 58K15, Secondary 32S30, 58K40 Let $(X,S)$ be an isolated complete intersection singularity of dimension $n$, and let $f:(X,S)\rightarrow (\mathbb{C}^{n+1},0)$ be a germ of $\mathscr{A}$-finite mapping. In this master's degree final project, our main contribution is that we show the case $n=2$ of the general Mond conjecture, which states that $μ_I(X,f)\geq \text{codim}_{\mathscr{A}_e}(X,f)$, with equality provided $(X,f)$ is weighted homogeneous. Before this project, the only known case for which the conjecture was known to hold is in the case that $n=1$ and $(X,S)$ is a plane curve. |
| title | Disentangling mappings defined on ICIS |
| topic | Algebraic Geometry Primary 58K15, Secondary 32S30, 58K40 |
| url | https://arxiv.org/abs/2403.19678 |