Galois Groups of Symmetric Cubic Surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911142921633792 |
|---|---|
| author | Pichon-Pharabod, Eric Telen, Simon |
| author_facet | Pichon-Pharabod, Eric Telen, Simon |
| contents | The Galois group of a family of cubic surfaces is the monodromy group of the 27 lines of its generic fibre. We describe a method to compute this group for linear systems of cubic surfaces using certified numerical computations. Applying this to all families which are invariant under the action of a subgroup of $S_5$, we find that the Galois group is often much smaller than the Weyl group $W(E_6)$. As a byproduct, we compute the discriminants of these~families. Our method allows to compute the monodromy representation on homology of any family of generically smooth projective hypersurfaces. To illustrate this broader scope, we include computations for symmetric quartic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Galois Groups of Symmetric Cubic Surfaces Pichon-Pharabod, Eric Telen, Simon Algebraic Geometry 14D05, 65H14 (Primary) 14Q10, 32S40, 32G20, 55R80 (Secondary) The Galois group of a family of cubic surfaces is the monodromy group of the 27 lines of its generic fibre. We describe a method to compute this group for linear systems of cubic surfaces using certified numerical computations. Applying this to all families which are invariant under the action of a subgroup of $S_5$, we find that the Galois group is often much smaller than the Weyl group $W(E_6)$. As a byproduct, we compute the discriminants of these~families. Our method allows to compute the monodromy representation on homology of any family of generically smooth projective hypersurfaces. To illustrate this broader scope, we include computations for symmetric quartic surfaces. |
| title | Galois Groups of Symmetric Cubic Surfaces |
| topic | Algebraic Geometry 14D05, 65H14 (Primary) 14Q10, 32S40, 32G20, 55R80 (Secondary) |
| url | https://arxiv.org/abs/2509.06785 |