2015-01-05

The Satake compactification

Reading the question "Have there been efforts to introduce non Greek or Latin alphabets into mathematics?" at Mathematics Stack Exchange, I noticed this in an answer by Dan Peterson:

Let X be a quotient of a bounded symmetric domain by an arithmetic group. [...] Namikawa tried to popularize the notation X for the Satake compactification. サ is katakana, the first initial of Satake. It did not stick.

Intriguing! I tried to find more on this, but the closest I got was Yuji Odaka's "Tropically compactify moduli via Gromov-Hausdorff collapse", which uses the notation X, with a footnote:

The character "さ" is Hiragana type character which we pronouce "SA", the first syllable of Satake and the idea of using this character is after Namikawa’s book [Nam2] which used Katakana "サ" instead (but we japaneses rarely use katakana for writing japanese name). The corresponding Kanji character 佐 is more normal.

So apparently part of the reason it did not stick is disagreement even within the Japanese-speaking mathematics community over which type of character to use. (You see? East Asian orthography really does retard the progress of the sciences!)

"[Nam2]" is a reference to this book:

[Nam2] Y. Namikawa, Toroidal Compactification of Siegel Spaces, Lecture Notes in Mathematics, vol. 812 (1980).

... which is, alas, not in any library collection I have easy access to and too expensive to buy for blog research. Here the trail went cold, in other words.

Popularity factor: 2

leoboiko:

Google only offers us tantalizing "snippets" of Namikawa, but it's enough to see that not only he used superscript サ to denote Satake compactification, but also distinguished Mumford compactification with superscript マ. From the look of it, he didn't skimp on other writing systems, either.


Matt:

Thanks! Google wouldn't even let me see snippets from my Japanese IP.

Aime la vérité, mais pardonne à l'erreur

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