Separated Belyi Maps
| Autor: | Scherr, Zachary, Zieve, Michael E. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Mathematical Research Letters 21 (2014), 1389-1406 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4310/MRL.2014.v21.n6.a10 |
| Popis: | We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q-bar, and any disjoint finite subsets S, T in C(Q-bar), we construct a finite morphism f: C -> P^1 such that f ramifies at each point in S, the branch locus of f is {0,1, infty}, and f(T) is disjoint from {0,1, infty}. This refines a result of Mochizuki's. We also prove an analogous result over fields of positive characteristic, and in addition we analyze how many different Belyi maps f are required to imply the above conclusion for a single C and S and all sets T in C(Q-bar) \ S of prescribed cardinality. Comment: 14 pages |
| Databáze: | arXiv |
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