Global index of real polynomials
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866914995904708608 |
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| author | Monsalve, Gabriel E. Tibăr, Mihai |
| author_facet | Monsalve, Gabriel E. Tibăr, Mihai |
| contents | We develop two methods for expressing the global index of the gradient of a 2 variable polynomial function $f$: in terms of the atypical fibres of $f$, and in terms of the clusters of Milnor arcs at infinity. These allow us to derive upper bounds for the global index, in particular refining the one found by Durfee in terms of the degree of $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16496 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global index of real polynomials Monsalve, Gabriel E. Tibăr, Mihai Algebraic Geometry Geometric Topology We develop two methods for expressing the global index of the gradient of a 2 variable polynomial function $f$: in terms of the atypical fibres of $f$, and in terms of the clusters of Milnor arcs at infinity. These allow us to derive upper bounds for the global index, in particular refining the one found by Durfee in terms of the degree of $f$. |
| title | Global index of real polynomials |
| topic | Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2303.16496 |