# Fortnightly links (81)

Enrico Fatighenti, Giovanni Mongardi: Fano varieties of K3 type and IHS manifolds is a very interestingn preprint, constructing many new examples where it can be expected that the geometry of a Fano variety and associated hyperkähler varieties is controlled by an admissible subcategory in the derived category. This phenomenon was first studied for cubic fourfolds and Gushel–Mukai fourfolds, and I'm looking forward to seeing these other cases being studied.

Daniel Bragg, Max Lieblich: Perfect points on genus one curves and consequences for supersingular K3 surfaces explains how the proof of Artin's conjecture might not be a proof after all. This conjecture states that supersingular K3 surfaces (which only exist in positive characteristic) are unirational (i.e. there is a dominant map from $\mathbb{P}^2$ onto the surface).

Timothy Perutz: The mirror's magic sights: an update on mirror symmetry is a wonderful introduction to mirror symmetry, covering its origin in physics, explaining the algebraic and symplectic geometry aspects, and recent developments.

He also writes

In this account I have not even touched on mirror symmetry for Fano manifolds [...]

, so let's hope mirror symmetry for them gets an equally nice article soon.