Flips from 4-folds with isolated complete intersection singularities. (English) Zbl 0923.14028
From the introduction: “The author investigates a flipping contraction \(g: X \rightarrow Y\) from a 4-fold \(X\) with at worst isolated singularities. If \(Y\) has an anti-bicanonical divisor (= bi-elephant) with only rational singularities, then \(g\) carries an inductive structure involving a chain of blow-ups (la torre pendente), and in particular, the flip exists. This naturally contains Reid’s “pagoda” as an anticanonical divisor (= elephant) and its proper transforms.”
There are recent developments due to Andreatta et al., and H. Takagi. Note that the existence of a minimal model for an algebraic variety of dimension \(\geq 4\) is still an open problem and its key part is the existence of flip.
There are recent developments due to Andreatta et al., and H. Takagi. Note that the existence of a minimal model for an algebraic variety of dimension \(\geq 4\) is still an open problem and its key part is the existence of flip.
Reviewer: De-Qi Zhang (Singapore)
MSC:
14J35 | \(4\)-folds |
14E30 | Minimal model program (Mori theory, extremal rays) |
14J17 | Singularities of surfaces or higher-dimensional varieties |