Quasi-projective varieties whose fundamental group is a free product of cyclic groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910887158218752 |
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| author | Cogolludo-Agustín, José Ignacio Elduque, Eva |
| author_facet | Cogolludo-Agustín, José Ignacio Elduque, Eva |
| contents | In this work we study smooth complex quasi-projective surfaces whose fundamental group is a free product of cyclic groups. In particular, we prove the existence of an admissible map from the quasi-projective surface to a smooth complex quasi-projective curve. Associated with this result, we prove addition-deletion Lemmas for fibers of the admissible map which describe how these operations affect the fundamental group of the quasi-projective surface. Our methods also allow us to produce curves in smooth projective surfaces whose fundamental groups of their complements are free products of cyclic groups, generalizing classical results on $C_{p,q}$ curves and torus type projective sextics, and showing how general this phenomenon is. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17282 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quasi-projective varieties whose fundamental group is a free product of cyclic groups Cogolludo-Agustín, José Ignacio Elduque, Eva Algebraic Geometry Geometric Topology 32S25, 32S55, 32S05, 32S20, 57K31 In this work we study smooth complex quasi-projective surfaces whose fundamental group is a free product of cyclic groups. In particular, we prove the existence of an admissible map from the quasi-projective surface to a smooth complex quasi-projective curve. Associated with this result, we prove addition-deletion Lemmas for fibers of the admissible map which describe how these operations affect the fundamental group of the quasi-projective surface. Our methods also allow us to produce curves in smooth projective surfaces whose fundamental groups of their complements are free products of cyclic groups, generalizing classical results on $C_{p,q}$ curves and torus type projective sextics, and showing how general this phenomenon is. |
| title | Quasi-projective varieties whose fundamental group is a free product of cyclic groups |
| topic | Algebraic Geometry Geometric Topology 32S25, 32S55, 32S05, 32S20, 57K31 |
| url | https://arxiv.org/abs/2210.17282 |