These are interesting times to look over the algebraic geometry arxiv postings. Just over a week ago, there was a posting by Tanaka which claimed the minimal model program was false in characteristic two. Then yesterday at the top of the page was a paper by Castravet and Tevelev claiming that the Mori Dream Space conjecture for 
I’ll keep my remarks brief here, but roughly a Mori Dream Space is an algebraic variety which “looks like” a toric variety, and so its birational geometry is strongly determined by some combinatorial invariants. There’s obviously much more to be said here, but for that I will defer to either the papers listed above or to a survey on Cox rings such as this one. The Mori Dream Space conjecture for a family of varieties 
One thing I can note here is that the object you most often study to get a handle on the birational geometry of 
Finally, even though a fly may drop, it may also start buzzing again, as noted by Ellenberg. Still, interesting stuff!
Charles Siegel
Jim Stankewicz
Matt DeLand
I’m looking for sources on
. (Not particularly interested in birational properties, more about singularities, stratifications and explicit descriptions.) I checked out the Fontanari paper in hope of finding useful references, but it doesn’t seem to discuss this quotient at all. Did you mean to refer to some other paper? In any case, do you know any good references about this quotient?
Thank you very much!
David Speyer