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The explanation for the name "moduli space" in the introduction is circular. What is a modulus (moduli?) supposed to be?--129.70.14.132 15:18, 23 June 2007 (UTC)[reply]

I'm a total beginner who'd like to know what a moduli space is. Nowhere in this article did I find a coherent definition or an example of what I moduli space is. It might be useful to write this with a view to including someone who doesn't know anything (like me). —Preceding unsigned comment added by 130.88.123.90 (talk) 09:18, 31 October 2007 (UTC)[reply]

Commenters above are correct. This article is in poor shape. I have rewritten the introduction, and intend to further clean up the article. 76.253.92.38 22 May 2008

I'm curious-- does anyone know why this is called a "moduli space" rather than a "modulus space"? It seems unusual to use the plural as a modifier. 65.185.17.187 (talk) 15:25, 9 April 2013 (UTC)[reply]

The key line is "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." ᛭ LokiClock (talk) 03:12, 18 April 2013 (UTC)[reply]

I don't think that answers the question. We don't use phrases like "vectors space", or "tangents bundle". Maybe it's because "moduli" is a strange plural, so the phrase "moduli space" doesn't sound so bad. — Preceding unsigned comment added by 2607:F140:400:1028:78BF:D11:6D2E:A302 (talk) 17:38, 6 October 2014 (UTC)[reply]

Currently satisfied with Introduction, and Basic Examples. Partially satisfied with Definitions. Later sections are a mess. 76.253.92.38 (talk) 02:18, 22 May 2008 (UTC)[reply]

I've cleaned up everything but the section on Further Examples, which is still a mess. 76.253.92.38 (talk) 19:00, 22 May 2008 (UTC)[reply]

In this chapter it is said,

"A fine moduli space is an object X, together with a family f:T \rightarrow X called the universal family, with the property that given any family g:A → B, there is a unique map φ(g):B → X such that the pullback of f along φ(g) is g. "

Shouldn't the "T" be an "A"? T is nowhere defined and not used again.--129.70.14.132 16:52, 23 June 2007 (UTC)[reply]

The comment(s) below were originally left at Talk:Moduli space/CommentsTalk:Moduli space/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Last edited at 11:23, 26 May 2007 (UTC). Substituted at 02:21, 5 May 2016 (UTC)

It would be useful to talk about atlas's of stacks and give the atlas for the module of vector bundles on a curve. See Page 81 of https://impa.br/wp-content/uploads/2017/04/PM_36.pdf Kaptain-k-theory (talk) 18:36, 21 May 2021 (UTC)[reply]

The article is full of apparently well-written and knowledgeable accounts of the theory behind moduli spaces.

What is completely wrong-headed is that this article completely fails to include a wealth of simple examples before rushing to include the highly advanced information that only 1% of 1% of Wikipedia readers will appreciate — if that many.