范畴归结、偏序集概型与DuBois奇点
Categorical resolutions, poset schemes and Du Bois singularities
摘要：
我们引入了偏序集概型的概念，并研究了这种空间上的拟凝聚层范畴。然后，我们表明，光滑偏序集计划可以用来获得通常的奇异方案的奇异性的分类决议。证明了奇异簇$X$具有这样的分解当且仅当$X$具有Du Bois奇点.最后，我们证明了代数簇$Y$的de Rham-Du Bois复形可以用满足经典拓扑中$Y$上的下降的任何光滑偏序集方案来定义.
英文摘要：
We introduce the notion of a poset scheme and study the categories of quasi-coherent sheaves on such spaces. We then show that smooth poset schemes may be used to obtain categorical resolutions of singularities for usual singular schemes. We prove that a singular variety $X$ possesses such a resolution if and only if $X$ has Du Bois singularities. Finally we show that the de Rham-Du Bois complex for an algebraic variety $Y$ may be defined using any smooth poset scheme which satisfies the descent over $Y$ in the classical topology.
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