# Giant Rat of Sumatra singularity

I would be grateful for explanations of the issues raised in any of these three questions, or pointers to the relevant literature (now updated with answers):

1. How did a particular singularity come to be known as The Giant Rat of Sumatra?
Answer: Named by Bruce & Giblin after a Sherlock Holmes reference, as explained by Michael Biro and Daniel Moskovitch.
2. What is the generic polynomial form of this singularity?
Answer: $f_a(x,y)=x y(x-y)(x-a y)$ for a parameter $a$. This from Daniel Moskovitch's answer to the MO question, "What are some examples of colorful language in serious mathematics papers?" Here is a plot for $a=\frac{1}{4}$. Despite its formidable name, the singularity appears rather tame to the eye:

3. Is there some natural equivalence relation that classifies all the giant-rat singularities into the same class (unlike Arnold's $\cal{A}$-equivalence, which in my [limited] understanding, does not).
Answer: On p.199, Bruce & Giblin say that the polynomial above "gives uncountably many inequivalent types" (for different parameters $a$). They address my question of another equivlance relation: "topological equivalence is too weak to provide a workable theory... Instead one has to work with 'universal stratified equivalence'," a theory due to Eduard Looijenga. They go on to say, "Even for the giant rat of Sumatra one has little idea what these models are. The world is indeed not yet prepared for its story." :-)

I ask this as someone largely ignorant of singularity theory. Thanks for enlightening me (and other MO participants)!

-
The giant rat of Sumatra is a Sherlock Holmes reference, where he mentions it as a story 'for which the world is not yet prepared'. –  Michael Biro Feb 19 '12 at 3:04
Perhaps the answer to your question is this: mathoverflow.net/questions/22299/… –  Daniel Moskovich Feb 19 '12 at 5:06
Probably with a sly reference to Holmes's fondness for the word "singular" when referring to anything unusual. –  Nate Eldredge Feb 19 '12 at 19:03

I believe all is answered by Page 196 (and the subsequent discussion) of Curves and Singularities by J.W. Bruce and P.J. Giblin, who coined the name.

-
Google books preview is missing the relevant pages, but you can see a (typically colorful) reference on page 291: books.google.com/… –  Graham Leuschke Feb 19 '12 at 11:16
@Daniel: Thanks! I will retrieve the Bruce-Giblin book and report back. –  Joseph O'Rourke Feb 19 '12 at 14:47