On the monodromy action for $f(x,y)=g(x)+h(y)$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914960938893312 |
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| author | Garcia, Daniel López Valencia, Fabricio |
| author_facet | Garcia, Daniel López Valencia, Fabricio |
| contents | We solve the problem of determining under which conditions the monodromy of a vanishing cycle generates the whole homology of a regular fiber for a polynomial $f(x,y)=g(x)+h(y)$ where $h$ and $g$ are polynomials with real coefficients having real critical points and satisfying $deg(g)\cdot deg(h)\leq 2500$ and $\gcd(deg(g),deg(h))\leq 2$. As an application, under the same assumptions we solve the tangential-center problem which is known to be linked to the weak 16th Hilbert problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05563 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the monodromy action for $f(x,y)=g(x)+h(y)$ Garcia, Daniel López Valencia, Fabricio Complex Variables Algebraic Topology 14D05, 32S40, 34M35 We solve the problem of determining under which conditions the monodromy of a vanishing cycle generates the whole homology of a regular fiber for a polynomial $f(x,y)=g(x)+h(y)$ where $h$ and $g$ are polynomials with real coefficients having real critical points and satisfying $deg(g)\cdot deg(h)\leq 2500$ and $\gcd(deg(g),deg(h))\leq 2$. As an application, under the same assumptions we solve the tangential-center problem which is known to be linked to the weak 16th Hilbert problem. |
| title | On the monodromy action for $f(x,y)=g(x)+h(y)$ |
| topic | Complex Variables Algebraic Topology 14D05, 32S40, 34M35 |
| url | https://arxiv.org/abs/2311.05563 |