


























Abstract:For a smooth algebraic curve defined over a number field, one can associate a bipartite graph called a dessin d'enfant.
We study the regularity and automorphism groups of dessins with uniform passports. In a previous paper, we proved that every passport of the form $[n,b^{q},n]$ of genus at least 2 admits a dessin with trivial automorphism group. Here we prove the analogous result for passports of the form $[b^{q},b^{q},n]$.
We also construct examples of uniform passports of genus at least 2 for which every dessin with that passport has nontrivial automorphism group, and others for which every dessin with that passport has trivial automorphism group.
Finally, we give an alternative proof of the $[n,b^{q},n]$ case using counting arguments based on centralizers of permutations.
From: Tatsuya Ohnishi [view email]
[v1]
Thu, 25 Jun 2026 14:56:42 UTC (1,003 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。