Wonderful compactification of an arrangement of subvarieties
Abstract
We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety Y and certain collection G of subvarieties of Y, the wonderful compactification YG can be constructed by a sequence of blow-ups of Y along the subvarieties of the arrangement. This generalizes the Fulton-MacPherson configuration spaces and the wonderful models given by De Concini and Procesi. We give a condition on the order of blow-ups in the construction of YG such that each blow-up is along a nonsingular center.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.