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51: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/06/27(土) 23:01:24.66 ID:jEjJjPRO

”Teichmuller space” 良く纏まっている
https://en.wikipedia.org/wiki/Teichm%C3%BCller_space
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
Main article: Bers slice

https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Bers-Einbettung.png/220px-Bers-Einbettung.png
Image of the Bers embedding of a punctured torus' 2-dimensional Teichmuller space

https://en.wikipedia.org/wiki/Moduli_of_algebraic_curves
Moduli of algebraic curves

つづく

http://rio2016.5ch.net/test/read.cgi/math/1592654877/51

52: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/06/27(土) 23:02:30.33 ID:jEjJjPRO

>>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

http://rio2016.5ch.net/test/read.cgi/math/1592654877/52

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