Inner rates of finite morphisms
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913259091656704 |
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| author | Cherik, Yenni |
| author_facet | Cherik, Yenni |
| contents | Let $(X, 0)$ be a complex analytic surface germ embedded in $(\mathbb{C}^n,0)$ with an isolated singularity and $Φ=(g,f):(X,0) \longrightarrow (\mathbb{C}^2,0)$ be a finite morphism. We define a family of analytic invariants of the morphism $Φ$, called inner rates of $Φ$. By means of the inner rates we study the polar curve associated to the morphism $Φ$ when fixing the topological data of the curve $(gf)^{-1}(0)$ and the surface germ $(X,0)$, allowing to address a problem called polar exploration. We also use the inner rates to study the geometry of the Milnor fibers of a non constant holomorphic function $f:(X,0) \longrightarrow (\mathbb{C},0)$. The main result is a formula which involves the inner rates and the polar curve alongside topological invariants of the surface germ $(X,0)$ and the curve $(gf)^{-1}(0)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02949 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inner rates of finite morphisms Cherik, Yenni Algebraic Geometry 32S25, 57M27 (Primary) 14B05, 32S55 (Secondary) Let $(X, 0)$ be a complex analytic surface germ embedded in $(\mathbb{C}^n,0)$ with an isolated singularity and $Φ=(g,f):(X,0) \longrightarrow (\mathbb{C}^2,0)$ be a finite morphism. We define a family of analytic invariants of the morphism $Φ$, called inner rates of $Φ$. By means of the inner rates we study the polar curve associated to the morphism $Φ$ when fixing the topological data of the curve $(gf)^{-1}(0)$ and the surface germ $(X,0)$, allowing to address a problem called polar exploration. We also use the inner rates to study the geometry of the Milnor fibers of a non constant holomorphic function $f:(X,0) \longrightarrow (\mathbb{C},0)$. The main result is a formula which involves the inner rates and the polar curve alongside topological invariants of the surface germ $(X,0)$ and the curve $(gf)^{-1}(0)$. |
| title | Inner rates of finite morphisms |
| topic | Algebraic Geometry 32S25, 57M27 (Primary) 14B05, 32S55 (Secondary) |
| url | https://arxiv.org/abs/2210.02949 |