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摘要翻译：
几乎Belyi覆盖是射影线的代数覆盖，使得除一个简单分支点外的所有分支点都位于射影线的一组3个点之上。一般说来，这些覆盖物有一个具有固定分支模式的一维族。（也就是说，这些覆盖的Hurwitz空间是曲线。）本文明确地构造了三个11、12和20度的几乎Belyi覆盖。我们证明了如何用这些覆盖来计算第六个Painleve方程的几个代数解。
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英文标题：
《Computation of highly ramified coverings》
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作者：
Raimundas Vidunas, Alexander Kitaev
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Classical Analysis and ODEs 经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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英文摘要：
An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of these coverings with a fixed ramification pattern. (That is, Hurwitz spaces for these coverings are curves.) In this paper, three almost Belyi coverings of degrees 11, 12, and 20 are explicitly constructed. We demonstrate how these coverings can be used for computation of several algebraic solutions of the sixth Painleve equation.
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PDF链接：
https://arxiv.org/pdf/0705.3134
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