| Title | Algorithms for Mumford curves |
| Author(s) | Ralph Morrison, Qingchun Ren |
| Type | Article in Journal |
| Abstract | Abstract Mumford showed that Schottky subgroups of PGL ( 2 , K ) give rise to certain curves, now called Mumford curves, over a non-archimedean field K. Such curves are foundational to subjects dealing with non-archimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p-adic numbers. A crucial and difficult step is finding a good set of generators for a Schottky group, a problem solved in this paper. This result allows us to design and implement algorithms for tasks such as: approximating the period matrices of the Jacobians of Mumford curves; computing the Berkovich skeleta of their analytifications; and approximating points in canonical embeddings. We also discuss specific methods and future work for hyperelliptic Mumford curves. |
| Keywords | Mumford curve, Tropical geometry |
| ISSN | 0747-7171 |
| URL |
http://www.sciencedirect.com/science/article/pii/S0747717114000819 |
| Language | English |
| Journal | Journal of Symbolic Computation |
| Volume | 68, Part 2 |
| Number | 0 |
| Pages | 259 - 284 |
| Year | 2015 |
| Note | Effective Methods in Algebraic Geometry |
| Edition | 0 |
| Translation |
No |
| Refereed |
No |
