• Claus Ringel, Quiver Grassmannians for wild acyclic quivers is an extension of the result that any projective variety can be realised as a quiver Grassmannian, showing that any wild acyclic quiver can be used (previous results by Zimmerman-Huisgen, Hille, and Reineke used a specific quiver). I have previously blogged about a silly implementation that performs these steps in the case of Reineke's construction, in case you want to see how it goes in detail.

  • Some excellent news: arXiv's TeX processing system receives significant upgrade.

  • Narasimhan, Derived categories of moduli spaces of vector bundles on curves is a paper that I've been wanting to see for a while. It is shows that $\mathbf{D}^{\mathrm{b}}(C)$ (where $C$ is any smooth projective curve of genus $g\geq 3$) can be embedded in the derived category of the moduli space of rank–2 vector bundles with fixed determinant of degree–1 (which is a Fano variety). I have previously mentioned the completely different Kuznetsov–Fonarev preprint proving the same result for a generic curve. Narasimhan's paper was earlier but not available as a preprint, and proves the result for all curves using vanishing results (which admittedly are a bit outside my comfort zone).

There seems to have been an issue, preventing this blogpost from being published on Sunday last week. Hopefully it appears now.