Speaker
Xianyu Hu
Description
Let $X \to S$ be a proper semistable degeneration. For the singular central fibre, the usual choices $D^b_{\mathrm{coh}}(X_0)$ and $\operatorname{Perf}(X_0)$ fail, in complementary ways, to be simultaneously smooth and proper. Inspired by the fact that the natural log structures make the degeneration log smooth, we define logarithmic coherent sheaves and the associated category of log perfect complexes. This category is proper over $S$ and satisfies a logarithmic version of categorical smoothness. I will outline the motivation and construction, using a nodal degeneration as a guiding example. This is joint work with Hannah Dell, Patrick Kennedy-Hunt, Kabeer Manali Rahul, and Maximilian Schimpf.