Talk:Morphism of algebraic varieties

Comment by B-80[edit]

Please let me apologize in advance for probably doing this wrong, I've never used the talk pages before on Wikipedia and don't really know Wiki formatting that well. But Regular function redirects here. I am not a mathematician, but the definition I needed is basically something along the lines of:

A function, f, is called regular at a point x if f is not singular at x.

I don't know if this is common mathematical usage of the term regular function, but I was unable to extract that meaning from this article. But because I clearly don't understand what this page is talking about I don't want to edit it. If the definition I wrote is valid (there's of course a chance that the book I'm reading is misusing the term because it's a physics text) it would really be great if someone could put something along the lines of what I wrote there without ruining the integrity of the page as I would if I tried to edit.

Thanks guys, again sorry if I have formatted this page wrong

B-80 (talk) 01:39, 17 July 2013 (UTC)[reply]

Polynomial functions are never singular. As for formatting, just title a new talk page section with the subject of the message, and write Regular function as [[Regular function]]. However, as alluded to at the end of the article, the term regular function or regular map may especially in older texts adapt to the broader class of smooth functions over the domain, such as the analytic functions when talking about the reals, and the holomorphic ones when talking about the complex numbers. ᛭ LokiClock (talk) 11:02, 17 July 2013 (UTC)[reply]

First of all, don't worry about the formatting. Second, the main issue here is that we are actually not giving a definition of regular map between open sets. This is tricky because an open subset of an affine variety need not be affine (C² minus the origin.) I've edited the article a bit, but in the end someone should actually consult the source and add the precise definitions to the article. -- Taku (talk) 14:16, 17 July 2013 (UTC)[reply]

Overly Sophisticated[edit]

This presentation of regular functions is just . . . ridiculous. Somebody grab Hartshorne and fix this garbage so that people can understand, rather than awe at the unintelligibility obtainable by the "author"(s) of this "article". — Preceding unsigned comment added by 138.26.73.89 (talk) 18:24, 9 September 2014 (UTC)[reply]

Actually we also give a definition of Hartshorne. I agree the definition looks complicated; it would be nice if someone knows a better way. By the way, the "correct official definition" is that a morphism of varieties is a morphism of "ringed spaces" underlying varieties (which is actually missing and I'm going to add it in a second.) -- Taku (talk) 02:11, 4 February 2015 (UTC)[reply]

"Ring of regular functions" listed at Redirects for discussion[edit]

An editor has identified a potential problem with the redirect Ring of regular functions and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 December 21 § Ring of regular functions until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Jay 💬 03:43, 4 January 2023 (UTC)[reply]