2010/11/28 by V. A. Lunts, Lunts, V. A.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1011.6089
Comments welcome
arxiv created 2010/11/28 · openalex publication_date 2010/11/28 · arxiv updated 2010/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.