Superelliptic curves with many automorphisms and CM Jacobians
| Autor: | Obus, Andrew, Shaska, Tony |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Math. Comp. 90 (2021), no. 332, 2951--2975 |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathcal{C}$ be a smooth, projective, genus $g\geq 2$ curve, defined over $\mathbb{C}$. Then $\mathcal{C}$ has \emph{many automorphisms} if its corresponding moduli point $p \in \mathcal{M}_g$ has a neighborhood $U$ in the complex topology, such that all curves corresponding to points in $U \setminus \{p \}$ have strictly fewer automorphisms than $\mathcal{C}$. We compute completely the list of superelliptic curves having many automorphisms. For each of these curves, we determine whether its Jacobian has complex multiplication. As a consequence, we prove the converse of Streit's complex multiplication criterion for these curves. Comment: Incorrect program file very_good_primes.sage replaced with stable_reduction.sage, no changes in article, still 24 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|