Special points on intersections of hypersurfaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914087814823936 |
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| author | Gómez-Gonzáles, Claudio |
| author_facet | Gómez-Gonzáles, Claudio |
| contents | We establish lower bounds on the ambient dimension for an intersection of hypersurfaces to have a dense collection of ``level $\ell$" points, in the sense introduced by Arnold-Shimura, given as a polynomial in the numbers of hypersurfaces of each degree. Our method builds upon the framework for solvable points of Gómez-Gonzáles-Wolfson to include other classes of accessory irrationality, towards the problem of understanding the arithmetic of "special points." We deduce improved upper bounds on resolvent degree $\operatorname{RD}(n)$ and $\operatorname{RD}(G)$ for the sporadic groups as part of outlining frameworks for incorporating future advances in the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special points on intersections of hypersurfaces Gómez-Gonzáles, Claudio Algebraic Geometry Group Theory Number Theory 14G05 (Primary), 14M15, 14L30, 20C34 We establish lower bounds on the ambient dimension for an intersection of hypersurfaces to have a dense collection of ``level $\ell$" points, in the sense introduced by Arnold-Shimura, given as a polynomial in the numbers of hypersurfaces of each degree. Our method builds upon the framework for solvable points of Gómez-Gonzáles-Wolfson to include other classes of accessory irrationality, towards the problem of understanding the arithmetic of "special points." We deduce improved upper bounds on resolvent degree $\operatorname{RD}(n)$ and $\operatorname{RD}(G)$ for the sporadic groups as part of outlining frameworks for incorporating future advances in the theory. |
| title | Special points on intersections of hypersurfaces |
| topic | Algebraic Geometry Group Theory Number Theory 14G05 (Primary), 14M15, 14L30, 20C34 |
| url | https://arxiv.org/abs/2510.10272 |