Fortnightly links (140)

Federico Caucci: Paracanonical base locus, Albanese morphism, and semi-orthogonal indecomposability of derived categories discusses a topic I'm a big fan of, namely indecomposability of derived categories. Recently Xun Lin brought the geometry of the paracanonical base locus to the forefront as a good tool to study this, and this paper continues that study, explaining a more conceptual take on this object, and obtaining new cases. Cool!

Nancy Abdallah, Jacques Emsalem, Anthony Iarrobino: Nets of conics and associated Artinian algebras of length 7 is an old preprint (from 1977!) that finally made its way to the arXiv, about nets of conics. It's a topic that is great fun, and features also in an interesting way in noncommutative algebraic geometry when discussing certain noncommutative projective planes. There's ample pictures to admire in this writeup too.

Yukinobu Toda: Derived categories of Quot schemes of locally free quotients via categorified Hall products gives a derived algebro-geometric proof of a semiorthogonal decomposition of (derived) Quot schemes of coherent sheaves. There's been a steady procession of ever more general versions, and this version is definitely a very general one.

This has many cool applications, such as for semiorthogonal decompositions of Brill–Noether loci, and also a description of $\mathbf{D}^{\mathrm{b}}(\operatorname{Hilb}^n\operatorname{Bl}_pS)$ for a surface $S$ (independently obtained by Naoki Koseki). Very cool!

The Koseki preprint is now available at Categorical blow-up formula for Hilbert schemes of points.