# Fortnightly links (60)

Luca Battistella, Francesca Carocci, Cristina Manolache: Virtual classes for the working mathematician is a nice set of lecture notes on virtual fundamental classes.

It's no secret I like semiorthogonal decompositions and exceptional collections, so let me tell you about Anton Fonarev: On the bounded derived category of $\mathrm{IGr}(3,7)$. It is expected that homogeneous varieties of the type $G/P$ have a full exceptional collection. Now the odd isotropic Grassmannian $\mathrm{IGr}(3,7)$ is

*not*a homogeneous variety (there's a non-reductive group here), but it's sufficiently close to it that the usual methods (i.e. Borel–Weil–Bott for the ordinary Grassmannian) can be applied to it, as it is the zero section of a vector bundle on the Grassmannian. The preprint constructs a minimal Lefschetz decomposition for the first case that was previously unknown, consisting of equivariant vector bundles.Boris Shoikhet is advertising a PhD position at the University of Antwerp.