Talk:Branched covering

Examples
Please keep the scheme theoretic examples on this page! The main problem with wikipedia math pages is the lack of useful examples. — Preceding unsigned comment added by 71.212.234.13 (talk) 02:56, 24 June 2017 (UTC)
 * These example would be useful if they where written for a wider audience. As they are, they can be understood only by people knowing scheme theory, and are thus of no use for others (see WP:TECHNICAL). D.Lazard (talk) 07:58, 24 June 2017 (UTC)
 * Let's have a separate section then for a scheme-theoretic interpretation. — Preceding unsigned comment added by 161.98.8.3 (talk) 17:33, 24 June 2017 (UTC)

Hurewicz Theory
There should be a discussion of Hurewicz theory on this page, or on a separate page. This should include the basic definitions, examples of monodromy representations, and a discussion of how the representation theory of the symmetric group relates to this subject. A good starting place looks like

http://www.math.colostate.edu/~renzo/IMPA.pdf — Preceding unsigned comment added by 97.122.75.155 (talk) 02:46, 1 August 2017 (UTC)


 * You refer to "Hurewicz theory" but the article you link to is about "Hurwitz theory".


 * Adolph Hurwitz (1904-56) and Witold Hurewicz (1859-1919) are two distinct mathematicians.


 * So: What are you talking about?71.37.182.254 (talk) 18:57, 15 November 2020 (UTC)

Circular definition
There is a circular definition with unramified covering, ramification locus and the definition of the open set W. — Preceding unsigned comment added by Rgc1994 (talk • contribs) 10:20, 11 April 2020 (UTC)

Article is missing a definition!!!
A math article needs a definition of its subject.

Unfortunately,

"a map is a branched covering if it is a covering map everywhere except for a nowhere dense set known as the branch set"

is not a definition. It is a rough description.

Nothing wrong with including a rough description — that is a very good idea. But it doesn't substitute for a definition.

I hope someone familiar with the subject can provide a definition, at least for the topological case.71.37.182.254 (talk) 18:40, 15 November 2020 (UTC)

Extremely bad writing
The section Ramification locus begins with this sentence:

"The set of exceptional points on $$W$$ is called the ramification locus (i.e. this is the complement of the largest possible open set $$W'$$)."

This is extremely bad writing. The phrase "the largest possible open set" doesn't mean anything, because it doesn't specify what kind of open set it is referring to.

(Of course, "the largest possible open set" without further specification is the entire space, and the complement of the entire space is not what the ramification locus is. That complement is the empty set.)71.37.182.254 (talk) 18:49, 15 November 2020 (UTC)

Terminology: branched/ramified
The article never defines the term "ramified". Is it equivalent to "branched"? Is an "unramified covering" a covering map? Some clarification is needed here. --Hife (talk) 13:51, 27 May 2021 (UTC)