Moduli space | Wikipedia audio article
Channel: wikipedia tts
Date: 28/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Moduli_space


00:00:45 1 Motivation
00:03:11 2 Basic examples
00:03:20 2.1 Projective space and Grassmannians
00:03:56 2.2 Chow variety
00:04:39 2.3 Hilbert scheme
00:05:00 3 Definitions
00:05:22 3.1 Fine moduli spaces
00:06:40 3.2 Coarse moduli spaces
00:07:54 3.3 Moduli stacks
00:09:57 4 Further examples
00:10:07 4.1 Moduli of curves
00:12:05 4.2 Moduli of varieties
00:14:03 4.3 Moduli of vector bundles
00:14:32 5 Methods for constructing moduli spaces
00:15:25 6 In physics
00:19:05 7 References



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SUMMARY
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In algebraic geometry, a moduli space  is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.  Such spaces frequently arise as solutions to classification problems:  If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space.  In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects.