The Gauss--skizze decomposition is a Goresky-MacPherson stratification
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866929349012226048 |
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| author | Combe, N. C. |
| author_facet | Combe, N. C. |
| contents | We consider a new stratification of the space of configurations of $n$ marked points on the complex plane. Recall that this space can be differently interpreted as the space $^{\rm D}{\rm Pol}_{n}$ of degree $n>1$ complex, monic polynomials with distinct roots, the sum of which is 0. A stratum $A_σ$ is the set of polynomials having $P^{-1}(\mathbb{R}\cup\imath\mathbb{R})$ in the same isotopy class, relative to their asymptotic directions. We show that this stratification is a Goresky--MacPherson stratification and that from thickening strata a good cover in the sense of Čech can be constructed, allowing an explicit computation of the cohomology groups of this space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_08411 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The Gauss--skizze decomposition is a Goresky-MacPherson stratification Combe, N. C. Algebraic Geometry We consider a new stratification of the space of configurations of $n$ marked points on the complex plane. Recall that this space can be differently interpreted as the space $^{\rm D}{\rm Pol}_{n}$ of degree $n>1$ complex, monic polynomials with distinct roots, the sum of which is 0. A stratum $A_σ$ is the set of polynomials having $P^{-1}(\mathbb{R}\cup\imath\mathbb{R})$ in the same isotopy class, relative to their asymptotic directions. We show that this stratification is a Goresky--MacPherson stratification and that from thickening strata a good cover in the sense of Čech can be constructed, allowing an explicit computation of the cohomology groups of this space. |
| title | The Gauss--skizze decomposition is a Goresky-MacPherson stratification |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1808.08411 |