Noninjectivity of the monodromy of certain equicritical strata
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912104657715200 |
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| author | Huxford, Peter Salter, Nick |
| author_facet | Huxford, Peter Salter, Nick |
| contents | An equicritical stratum is the locus of univariate monic squarefree complex polynomials where the critical points have prescribed multiplicities. Tracking the positions of both roots and critical points, there is a natural ``monodromy map'' taking the fundamental group into a braid group. We show here that when there are exactly two critical points, this monodromy map is noninjective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noninjectivity of the monodromy of certain equicritical strata Huxford, Peter Salter, Nick Geometric Topology Algebraic Geometry An equicritical stratum is the locus of univariate monic squarefree complex polynomials where the critical points have prescribed multiplicities. Tracking the positions of both roots and critical points, there is a natural ``monodromy map'' taking the fundamental group into a braid group. We show here that when there are exactly two critical points, this monodromy map is noninjective. |
| title | Noninjectivity of the monodromy of certain equicritical strata |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2411.02222 |