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51(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/06/27(土)23:01 ID:jEjJjPRO(7/10) AAS
”Teichmuller space” 良く纏まっている
外部ﾘﾝｸ:en.wikipedia.org
Teichmuller space
The geometric vein in the study of Teichmuller space was revived following the work of William Thurston in the late seventies, who introduced a geometric compactification which he used in his study of the mapping class group of a surface.
Other more combinatorial objects associated to this group (in particular the curve complex) have also been related to Teichmuller space, and this is a very active subject of research in geometric group theory.
Quadratic differentials and the Bers embedding
Main article: Schwarzian derivative
省6
52(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/06/27(土)23:02 ID:jEjJjPRO(8/10) AAS
>>51
つづき
In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem.
The most basic problem is that of moduli of smooth complete curves of a fixed genus. Over the field of complex numbers these correspond precisely to compact Riemann surfaces of the given genus, for which Bernhard Riemann proved the first results about moduli spaces, in particular their dimensions ("number of parameters on which the complex structure depends").
Genus 1
Main article: Moduli stack of elliptic curves
つづく
56: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/06/28(日)16:25 ID:bfBvt+85(2/6) AAS
>>51
>画像ﾘﾝｸ[png]:upload.wikimedia.org
>Image of the Bers embedding of a punctured torus' 2-dimensional Teichmuller space
この図と川平 友規 外部ﾘﾝｸ[html]:www.math.titech.ac.jp
基礎講座・複素関数（『数学セミナー』2014年4月号〜2015年3月号）
複素関数論の基礎から初めて， 後半はリーマン面について解説しました．
第12回( 2015年3月号) 群で作るリーマン面
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