Fortnightly links (134)

Xun Lin: On nonexistence of semi-orthogonal decompositions in algebraic geometry gives an upgraded indecomposability criterion for derived categories of smooth projective varieties (and even some singular ones), which allows them to prove that ${\mathbf{D}}^{\mathrm{b}}({\mathrm{Sym}}^{i}C)$ is indecomposable for $i\le g-1$. That is a great result that I was hoping would see a proof soon!

Qingyuan Jiang: Derived categories of Quot schemes of locally free quotients, I is a great (in content and size) preprint constructing semiorthogonal decompositions for many situations in algebraic geometry, which somehow involve a Quot scheme. This will certainly lead to interesting applications.

Maxim Smirnov: On the derived category of the adjoint Grassmannian of type F tops of a very semiorthogonal fortnightly links, with Maxim constructing a full exceptional collection for the adjoint Grassmannian in type F₄. Based on the methods I can hope that we see E₆/P₂ and E₇/P₇ (and maybe E₇/P₁ and even E₈/P₈) being tackled soon too. The may you live in interesting times was cast upon me when it comes to this exciting question!