Talk:Moduli space

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Name origin[edit]

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]

Article Clean-Up[edit]

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]

Fine versus coarse moduli spaces[edit]

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]

Assessment comment[edit]

The comment(s) below were originally left at Talk: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.

Differentiate initial paragraphs into a lead and an introductory section. Add some historical context and references. Geometry guy 22:08, 20 May 2007 (UTC) Additional comments: too heavily slanted towards the technical side of the geometric invariant theory, at the expense of motivations and applications. Big disconnect between the start (elliptic curves) and the bulk of the article. Arcfrk 11:23, 26 May 2007 (UTC)[reply]

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

Some additions[edit]

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]