2017/07/13 by Andrei Baran, Baran, Andrei
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1707.04309
openalex publication_date 2017/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a generalization of the Dolbeault-Grothendieck resolution on a singular complex space. The same construction yields, for each morphism of analytic spaces, a pullback mapping between the respective Dolbeault-Grothendieck resolutions. As in the smooth case, the terms of the resolution are soft sheaves with stalks which are flat with respect to the sheaf of holomorphic sections. If, moreover, the complex space (X,OX) is countable at infinity then the global section spaces of the terms of the resolution are endowed with natural Fréchet-Schwarz topologies which induce the natural topology on the cohomology groups H\bullet (X,OX). The construction is an exercise in globalization using semi-simplicial techniques. Using the above construction one can produce, for instance, a soft resolution with OX-flat stalks for the de Rham complex on the analytic space X.