2019/06/16 by Michael McQuillan, McQuillan, Michael, Gianluca Marzo +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1906.06745
openalex publication_date 2019/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main theorem, I.a, is the existence for excellent Deligne-Mumford champ of characteristic zero of a resolution functor independent of the resolution process itself. Perceived wisdom was that this was impossible, but the counterexamples overlooked the possibility of using weighted blow ups. The fundamental local calculations take place in complete local rings, and are elementary in nature, while being self contained and wholly independent of Hironaka's methods and all derivatives thereof, i.e. existing technology. Nevertheless Abramovich, Temkin, and Wlodarczyk, [ATW], have varied existing technology to obtain an even shorter proof of principalisation, I.f, in the geometric case. Excellent patching is more technical than varieties over a field, and whence easier geometric arguments are pointed out when they exist.