# Fortnightly links (146)

Arend Bayer, Emanuele Macrì: The unreasonable effectiveness of wall-crossing in algebraic geometry is another ICM contribution, about Bridgeland stability and wall-crossing. The focus is largely on the phenomena arising for moduli of objects in K3 categories, and their applications to the geometry of hyperkähler varieties.

Naoki Koseki, Genki Ouchi: Perverse schobers and Orlov equivalences constructs perverse schobers enriching the mirror symmetry for elliptic curves. This was the first established case of homological mirror symmetry, and this preprint is a very nice and readable account of how perverse schobers enter the picture for this case. Cool!

Thorsten Beckmann, Jieao Song: Second Chern class and Fujiki constants of hyperkähler manifolds gives a short list of possible Betti numbers of hyperkähler fourfolds, subject to a reasonable conjecture. Two of them are well-known ($\mathrm{b}_{2,3,4}=23,0,276$ and $\mathrm{b}_{2,3,4}=7,8,108$ correspond to $\mathrm{K3}^{[2]}$- resp. $\mathrm{Kum}_2$-type), two of them do not correspond to a known construction. Are there types of hyperkähler fourfolds we don't know yet?! I hope that there are breakthroughs soon (either constructions or a proof that we have them all), the suspense is killing me!

Laura Pertusi, Paolo Stellari: Categorical Torelli theorems: results and open problems is a nice survey paper about how (subcategories of) derived categories of smooth projective varieties can govern the geometry of the varieties. This includes reconstruction results (i.e. for the entire category) but also constructing the original variety (or related varieties) as moduli spaces of Bridgeland-stable objects, going full circle with these fortnightly links to the first item.