整合法平面曲线上点的希尔伯特概型的半正交不可分解性
Semiorthogonal indecomposability for Hilbert schemes of points on integral locally planar curves
AI总结：
该研究针对代数闭域上具局部平面奇点的整射影曲线的点希尔伯特概型，证明其相关范畴的半正交不可分解性，建立了相对结论，结果适用于任意特征。
AI中文摘要：
设C是代数闭域上算术亏格为g、具局部平面奇点的整射影曲线。我们证明对每个1≤n≤g-1，$\boldsymbol{\text{Perf}}(\boldsymbol{\text{Hilb}}^n(C))$与$\boldsymbol{\text{D}^b_{\text{coh}}}(\boldsymbol{\text{Hilb}}^n(C))$均为半正交不可分解；还对连通基S上此类曲线的平坦族建立了对应的相对S-线性结论，其中$\boldsymbol{\text{D}^b_{\text{coh}}}$情形需满足容许性条件，结果在任意特征下成立。
英文摘要：
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.
