Talk:Function of several complex variables: Difference between revisions

Content deleted Content added
Line 35:
:(R. C. Gunning and Raghavan Narasimhan, Immersion of open Riemann surfaces, Math. Annalen 174 (1967), 103–108.)
:Therefore I will correct the text to reflect this fact. [[Special:Contributions/2601:200:C000:1A0:9AE:98DB:C7E0:3910|2601:200:C000:1A0:9AE:98DB:C7E0:3910]] ([[User talk:2601:200:C000:1A0:9AE:98DB:C7E0:3910|talk]]) 18:58, 28 December 2022 (UTC)
 
== Please say what you mean by superscript n ==
 
The definition of a '''coherent sheaf''' is given as follows:
 
"''The definition of the coherent sheaf is as follows.{{R|Serre1955|}}
 
A '''coherent sheaf''' on a [[ringed space]] <math>(X, \mathcal O_X)</math> is a sheaf <math>\mathcal F</math> satisfying the following two properties:
<ol type="1">
<li> <math>\mathcal F</math> is of ''finite type'' over <math>\mathcal O_X</math>, that is, every point in <math>X</math> has an [[open neighborhood]] <math>U</math> in <math>X</math> such that there is a surjective morphism <math>\mathcal{O}_X^n|_{U} \to \mathcal{F}|_{U} </math> for some natural number <math>n</math>;</li>
<li> for arbitrary open set <math>U\subseteq X</math>, arbitrary natural number <math>n</math>, and arbitrary morphism <math>\varphi: \mathcal{O}_X^n|_{U} \to \mathcal{F}|_{U} </math> of <math>\mathcal O_X</math>-modules, the kernel of <math>\varphi</math> is of finite type.</li>
</ol>''" [[Special:Contributions/2601:200:C082:2EA0:E1A8:CCAE:61A1:827C|2601:200:C082:2EA0:E1A8:CCAE:61A1:827C]] ([[User talk:2601:200:C082:2EA0:E1A8:CCAE:61A1:827C|talk]]) 02:19, 9 February 2023 (UTC)