Talk:Siegel modular variety

DYK nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Cwmhiraeth (talk) 06:41, 7 September 2019 (UTC)

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• ... that Siegel modular varieties are higher-dimensional analogues of moduli of algebraic curves, the focus of the Witten conjecture in quantum gravity, and were initially used to prove the Mordell conjecture in arithmetic geometry? Hulek, Klaus; Sankaran, G. K. (2002). "The Geometry of Siegel Modular Varieties". Advanced Studies in Pure Mathematics. 35: 89–156. and Cornell, Gary; Silverman, Joseph H., eds. (1986). Arithmetic geometry. Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30 – August 10, 1984. New York: Springer-Verlag. doi:10.1007/978-1-4613-8655-1. ISBN 0-387-96311-1. MR 0861969.
  • ALT1:... that although Siegel modular varieties play a central role in the Mordell conjecture and Siegel modular forms in arithmetic geometry, they also generalize moduli of algebraic curves, which are at the heart of open questions in quantum gravity, to higher dimensions? Hulek, Klaus; Sankaran, G. K. (2002). "The Geometry of Siegel Modular Varieties". Advanced Studies in Pure Mathematics. 35: 89–156. and Cornell, Gary; Silverman, Joseph H., eds. (1986). Arithmetic geometry. Papers from the conference held at the University of Connecticut, Storrs, Connecticut, July 30 – August 10, 1984. New York: Springer-Verlag. doi:10.1007/978-1-4613-8655-1. ISBN 0-387-96311-1. MR 0861969.
  • ALT2:... that Siegel modular varieties can be viewed as both an algebraic variety and a complex analytic space due to Jean-Pierre Serre's GAGA? Hulek, Klaus; Sankaran, G. K. (2002). "The Geometry of Siegel Modular Varieties". Advanced Studies in Pure Mathematics. 35: 89–156.
  • ALT3:... that the main idea of Faltings' proof of the Mordell conjecture is the study of heights on Siegel modular varieties? "Faltings relates the two notions of height by means of the Siegel moduli space.... It is the main idea of the proof." page 44 of Bloch, Spencer, The Proof of the Mordell Conjecture, The Mathematical Intelligencer, 6(2):41-47, 1984.
  • ALT4:... that Siegel modular varieties naturally capture information about black hole entropy in string theory? "This is a situation where there has been remarkable success in accounting for the entropy of black holes in string theory not only at leading order, but also various classes of subleading corrections... the function that naturally captures the microstates is a Siegel Modular Form (SMF)." in Section 1 and "This shows how we can easily build and characterize [Siegel modular forms] that have the potential to describe black holes or other gravitational systems." Section 5 of Belin, Alexandre; Castro, Alejandra; Gomes, João; Keller, Christoph A. (11 April 2017). "Siegel modular forms and black hole entropy" (PDF). Journal of High Energy Physics. 2017 (4). arXiv:1611.04588. doi:10.1007/JHEP04(2017)057.

• Reviewed: Exempt - nominator has fewer than five DYK credits.

Converted from a redirect by MarkH21 (talk). Self-nominated at 10:28, 26 August 2019 (UTC).

• Oh, dear. I salute your chutzpah in nominating an advanced math article for DYK. The date and the length of the article are OK. The main hook and ALT1 are well over the 200 character limit. The main problem, however, is with the proposed hooks themselves, and with how they are referenced in the article. As a mathematician myself, I sympathize with your predicament. However, we can't have a hook, where most readers would understand almost nothing in the statement of the hook, going to the main page. The hook needs to be short and as general as possible. Direct it towards a high school student interested in math. Smething along the lines of "that Siegel modular forms played a key role in Faltings' proof of the Mordell conjecture", or "that Siegel modular forms are related to open problems in quantum gravity", or some such thing. Note that the hook also needs to concentrate on a single fact rather than 5-6 different facts, as your ALT1 does. Next: The specific sentence in the article used to support the hook (and it must be a specific single centence, with a specific citation ref in it), must be sourced to a specific single secondary source (not two sources, like your main hook and your ALT1 do) that explicitly makes the statement mentioned in the hook. That is, once you come up with a reasonably general audience hook, you will need to find a book or a survey paper or a research article on the topic, where there is a specific sentence (or, at worst, 2-3 sentences) that explicitly supports what the hook says. You must be able to point out to such a sentence/sentences in the source when making a DYK nomination. In research math papers, the introductions often contain the relevant language. For survey/expository papers and books, it may be in a relevant section/chapter. I have not looked at the sources you propose in the nomination above to see if one could fish out a relevant supporting sentence there; you'll have to do that yourself once you come up with a better general hook. But it is insufficient to source the hook to a 67-page paper, like the Hulek-Sankaran paper, without specifying where exactly in that paper an uninitiated reader is supposed to look for the relevant statement. Moreover, for an advanced technical topic like this one, you would probably need to include a quote of the supporting sentence from the source in the reference in the article that is used to support the hook. (I don't mean including a supporting quote in the WP article itself, but rather in the reference.) Good luck! Nsk92 (talk) 12:04, 3 September 2019 (UTC)

• @Nsk92: Thanks for your comments! I agree that these hooks were a bit ambitious... I’ll propose ALT3 now and I’ll give a source for the statement soon! This should be much more suitable for a general audience. — MarkH21 (talk) 19:21, 3 September 2019 (UTC)

• Ok, very good, thanks! Nsk92 (talk) 19:23, 3 September 2019 (UTC)

• @Nsk92: Revised ALT3 and provided a specific ref. — MarkH21 (talk) 21:10, 3 September 2019 (UTC)

In formal sense, the ALT3 hook is better, and the source quoted is directly on point. However, I would still prefer a less technical hook. ALT3 hook mentions three highly technical things that most people won't know anything about and won't be able to understand: Faltings' theorem, height function and Siegel modular variety. It would be good to keep the number of such topics in the hook down to two. Also, I still think that if you can come up with a hook that mentions quantum gravity, that would make the hook much more appealing to a wider adience. Nsk92 (talk) 21:26, 3 September 2019 (UTC)

My concern is that the applications to physics are very indirect and hypothetical. The relation to the Witten conjecture stems purely from the fact that it generalizes the object that the conjecture describes. Meanwhile, the relation to black hole entropy is from the fact that some Siegel modular forms encapsulate information about black hole entropy in a particular string theory system, and Siegel modular forms are understood via Siegel modular varieties. On the other hand, they have a proven critical role in the proof of the Mordell conjecture. I've included ALT4 for your perusal though. — MarkH21 (talk) 21:43, 3 September 2019 (UTC)

I love ALT4! I understand your point re the Mordell conjecture, but for most Wikipedia readers the connection with black holes is much more interesting. I think the first quote you provide from Section 1 of Belin et al paper is good enough to justify the hook; and the fact that the source is called "Siegel modular forms and black hole entropy" helps too. I'll take a closer look at the rest of the article (although I don't promise to do that today). One quick comment. The caption below the picture of the Calabi-Yau quintic needs some kind of sourcing since the caption makes a mathematical statement. Nsk92 (talk) 22:02, 3 September 2019 (UTC)

Sure, I can certainly see so but it feels ever so slightly sensationalist - but maybe that's my demand for rigor speaking... and WP DYK hooks don't need to be the most rigorous :) I added the source for the caption, which was just reflecting what was in the "Properties" section already. — MarkH21 (talk) 22:19, 3 September 2019 (UTC)

OK, very good, thanks! A couple of other things. The statement in the lede that the notion was named after Carl Ludwig Siegel needs to be sourced to something (even if this fact is obvious to everyone familiar with the notion). Also, I could not unparse the last sentence in the lede: "Siegel modular varieties play a central role in the theory of Siegel modular forms which generalize classical modular forms and generalize moduli spaces of algebraic curves to higher dimensions." Specifically, it is grammatically unclear to what the second occurrence of "generalize" refers, Siegel modular varieties or Siegel modular forms. Also, this sentence, or at least the first part of it, needs to be sourced to something too. Nsk92 (talk) 22:27, 3 September 2019 (UTC)

Done! I hope it's clearer now! Thanks again for the useful comments, by the way.— MarkH21 (talk) 22:39, 3 September 2019 (UTC)

OK, very good, thanks. I'll take a closer look at the article tomorrow afternoon to check for other things. Also, if you know of some source (not necessarily published), such as lecture notes, a preprint, talk slides, or a published source, providing a good introduction to the topic, such an item/items could be added under Externals links (or Further reading, if the source is published). Nsk92 (talk) 22:51, 3 September 2019 (UTC)

I did a closer read through. Mostly everything looks pretty good. Well referenced, no clopping or copyright issues, the copyright status of the image checks out, no issues with OR. I added some missing doi numbers and several wikilinks. Pity that there is still no WP article about the Shafarevich finiteness conjecture. One minor thing that still needs fixing: please add the full publication details for ref no. 4 by Milne. If there are any green open access versions (arXiv, NSF-PAR, other preprint servers or institutional open access repositories, etc) of any of the sources beyond ref no 10, it would be nice to add the relevant links. Thanks, Nsk92 (talk) 10:50, 4 September 2019 (UTC)

Yes, there’s no full article about the Shafarevich finiteness conjecture but there’s a small bit said about it in the Mordell conjecture article. For Milne, there is a traditionally published version (as a chapter of “Harmonic analysis, the trace formula, and Shimura varieties” published in the Clay Math Proceedings Vol 4 in 2003) which we can use but the one I used a set of updated online notes (last updated 2017) published on Milne’s website. His online notes are standard references and are well-cited in research literature which demonstrates its reliability, if that is what you are concerned with. I’ll look for OA links (but I doubt they exist for most of the refs since they’re quite old) and another survey article. — MarkH21 (talk) 18:53, 4 September 2019 (UTC)

Re Milne: Since DYK articles are linked at the WP main page, the sourcing standards are more strict, and a self-published sources like online notes should not be used in references in this case. So please use the published Clay version as a reference (even if it is an offline source as it appears to be). The online notes may be listed in the Exernal links section in the article. Thanks, Nsk92 (talk) 19:30, 4 September 2019 (UTC)

Changed the Milne ref to the print version, but with a link to the freely available PDF on Clay’s website. — MarkH21 (talk) 19:52, 4 September 2019 (UTC)

OK, super! I'll double-check everything again, to make sure, and if nothing else comes up, I'll approve the nomination. Thanks, Nsk92 (talk) 19:55, 4 September 2019 (UTC)

OK, done and done! Thanks, Nsk92 (talk) 20:21, 4 September 2019 (UTC)

Thanks for all of the help! — MarkH21 (talk) 20:59, 4 September 2019 (UTC)

General: Article is new enough and long enough
New enough: Long enough:

Policy: Article is sourced, neutral, and free of copyright problems
Adequate sourcing: Neutral: Free of copyright violations, plagiarism, and close paraphrasing:

Hook: Hook has been verified by provided inline citation
Cited: Interesting:

QPQ: None required.

Overall: Approving ALT4 hook. Nsk92 (talk) 20:19, 4 September 2019 (UTC)