Genuinely ramified maps and monodromy
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916093479616512 |
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| author | Biswas, Indranil Kumar, Manish Parameswaran, A. J. |
| author_facet | Biswas, Indranil Kumar, Manish Parameswaran, A. J. |
| contents | For any genuinely ramified morphism $f\, :\, Y\, \longrightarrow\, X$ between irreducible smooth projective curves we prove that $\overline{(Y\times_X Y) \setminus Δ}$ is connected, where $Δ\, \subset\, Y\times_X Y$ is the diagonal. Using this result the following are proved:
If $f$ is further Morse then the Galois closure is the symmetric group $S_d$, where $d\,=\, \text{degree}(f)$.
The Galois group of the general projection, to a line, of any smooth curve $X\,\subset\, \PP^n$ of degree $d$, which is not contained in a hyperplane and contains a non-flex point, is $S_d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Genuinely ramified maps and monodromy Biswas, Indranil Kumar, Manish Parameswaran, A. J. Algebraic Geometry 14H30, 14G17, 14H60 For any genuinely ramified morphism $f\, :\, Y\, \longrightarrow\, X$ between irreducible smooth projective curves we prove that $\overline{(Y\times_X Y) \setminus Δ}$ is connected, where $Δ\, \subset\, Y\times_X Y$ is the diagonal. Using this result the following are proved: If $f$ is further Morse then the Galois closure is the symmetric group $S_d$, where $d\,=\, \text{degree}(f)$. The Galois group of the general projection, to a line, of any smooth curve $X\,\subset\, \PP^n$ of degree $d$, which is not contained in a hyperplane and contains a non-flex point, is $S_d$. |
| title | Genuinely ramified maps and monodromy |
| topic | Algebraic Geometry 14H30, 14G17, 14H60 |
| url | https://arxiv.org/abs/2401.08526 |