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


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.


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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