Semiorthogonal indecomposability for Hilbert schemes of points on integral locally planar curves

Qingyuan Jiang; Xun Lin

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arXiv · 2608.11608

Semiorthogonal indecomposability for Hilbert schemes of points on integral locally planar curves

Qingyuan Jiang·Xun Lin

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Abstract

Let $C$ be an integral projective curve of arithmetic genus $g$ with locally planar singularities over an algebraically closed field. We prove that for every $1\leq n\leq g-1$, both $\mathrm{Perf}(\mathrm{Hilb}^n(C))$ and $\mathrm{D^b_{coh}}(\mathrm{Hilb}^n(C))$ are semiorthogonally indecomposable. We also establish the corresponding relative $S$-linear statement for a flat family of such curves over a connected base $S$, with admissibility required in the $\mathrm{D^b_{coh}}$ case. Our results hold in arbitrary characteristic.

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BibTeX RIS

Qingyuan Jiang, Xun Lin. 2026-08-12. Semiorthogonal indecomposability for Hilbert schemes of points on integral locally planar curves. https://arxiv.org/abs/2608.11608

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