# Fortnightly links (131)

Peter Scholze: Half a year of the Liquid Tensor Experiment: Amazing developments is the public announcement of what I mentioned in the last fortnightly links, that the technical part of the Liquid Tensor Experiment has been successful. Congratulations to Johan Commelin for leading this effort, and for getting a DFG grant to continue working on this!

exlean is a blog about using Lean to prove theorems, and seems like an excellent resource to get familiar with the concepts and tools.

Alex Degtyarev, Ilia Itenberg, John Christian Ottem: Planes in cubic fourfolds shows that the maximum number of planes in a cubic fourfold (generically there are none!) is 405. Recall that on a cubic surface there are always 27 lines, on a quartic surface there are up to 64 lines.

I wonder whether the existence of multiple planes in a cubic fourfold implies something for the Kuznetsov component of its derived category, which is known to be equivalent to the derived category of a K3 surface (which relates to the rationality of cubic fourfolds containing planes). After all, a line on a K3 surface gives rise to a spherical autoequivalence. Or is there maybe something interesting happening with the Fano variety of lines on the cubic fourfold, which is a 4-dimensional hyperkähler variety?