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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bolza surface ： ウィキペディア英語版 Bolza surface In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (named after Oskar Bolza), is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely 48. An affine model for the Bolza surface can be obtained as the locus of the equation :$y^2=x^5-x$ in $\backslash mathbb\; C^2$. The Bolza surface is the smooth completion of the affine curve. Of all genus 2 hyperbolic surfaces, the Bolza surface has the highest systole. As a hyperelliptic Riemann surface, it arises as the ramified double cover of the Riemann sphere, with ramification locus at the six vertices of a regular octahedron inscribed in the sphere, as can be readily seen from the equation above. ==Triangle surface== The Bolza surface is a (2,3,8) triangle surface – see Schwarz triangle. More specifically, the Fuchsian group defining the Bolza surface is a subgroup of the group generated by reflections in the sides of a hyperbolic triangle with angles $\backslash tfrac,\; \backslash tfrac,\; \backslash tfrac$. More specifically, it is a subgroup of the index-two subgroup of the group of reflections, which consists of products of an even number of reflections, which has an abstract presentation in terms of generators $s\_2,\; s\_3,\; s\_8$ and relations $s\_2^8=1$ as well as $s\_2\; s\_3\; =\; s\_8$. The Fuchsian group defining the Bolza surface is also a subgroup of the (3,3,4) triangle group, which is a subgroup of index 2 in the (2,3,8) triangle group. It is interesting to note that the (2,3,8) group does not have a realisation in terms of a quaternion algebra, but the (3,3,4) group does. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bolza surface」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.