Pieter Belmans
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Fortnightly links (134)

Jul 26, 2021 • Pieter Belmans

posted in:
  • mathematics
tags:
  • fortnightly links
  • 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 $\mathbf{D}^{\mathrm{b}}(\operatorname{Sym}^iC)$ is indecomposable for $i\leq g-1$. 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!

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