Moduli space of curves | Wikipedia audio article
Channel: wikipedia tts
Date: 17/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Moduli_of_algebraic_curves


00:00:56 1 Moduli stacks of stable curves
00:02:49 2 Coarse moduli spaces
00:03:23 3 Moduli of marked curves
00:04:17 4 Boundary geometry
00:05:47 5 See also
00:07:52 6 References



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SUMMARY
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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").