Incarnations of the MMP

As was alluded to in my last post, my MMP talk is nearly upon me (if President’s day doesn’t intervene, that is). I think that I will make a habit of posting my talk notes here around the time I am giving each talk so, as a first instalment of this practice, here is the extended edition of my notes on the MMP.

I’m intrigued by this idea generally ascribed to Mori and Reid to allow a ‘Goldilocks’ class of singularities – wild enough to encompass what contractions in high dimensions could do, mild enough to be manageable by the machinery of the MMP – into the picture in order to develop a reasonable existence theory for minimal models. I hope to write something soon about the singularities appearing in the MMP – terminal singularities, canonical singularities, log versions of each of these,… – soon.

There are also a few words at the end of my notes on the ‘homological MMP’ developed by Michael Wemyss among others. I haven’t had much time to explore the topic deeply, but I find the ties between quiver GIT and the MMP enticing; especially after hearing in several talks in the UK how the former can be used to attack and interpret generalisations of the McKay correspondence.

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