# Fortnightly links (82)

Alexander Kuznetsov: On 5-dimensional minifolds and their Hilbert schemes of lines is part of the (preliminary) Oberwolfach proceedings for a workshop in July 2018, but I only found it recently. It summarises some nice results on 5-dimensional minifolds, which are varieties that have a Grothendieck group of minimal size, i.e. the rank is equal to the dimension plus 1. A classification of these is not yet available in dimension 5, and only five examples are known. But his abstract explains what happens if you take Hilbert schemes of lines on them: for all but one you get back another minifold, except in 1 case, whose derived category is conjectured to contain a Gushel–Mukai 5-fold. Fun!

Making of Byrne’s Euclid is a blogpost about an online version of Byrne's colourful version of the Euclid, and the challenges which in appear in doing so. It is a very enjoyable read about one of the prettiest typeset books I have seen, and it makes me appreciate that with the Stacks project we only intended to approximate on the web a LaTeX-produced pdf without any graphics (aside from commutative diagrams).

Benjamin Hennion: Tangent of K-theory explains in which way cyclic homology can be seen as the tangent space to algebraic K-theory. This makes precise in which way cyclic homology is meant to approximate algebraic K-theory.

The abelian deformation problems which appear in the abstract (and the article) are

*not*deformations of abelian categories by the way. The article works for arbitrary dg algebras, and abelian deformation problems refer to the structure of the dg Lie algebra associated to the formal moduli problem which arises from the tangent of K-theory.