Factoring 3-fold flips and divisorial contractions to curves

TL;DR

This paper demonstrates that complex 3-fold flips and divisorial contractions to curves can be decomposed into simpler geometric operations like weighted blow-ups, flops, and blow-downs, aiding understanding of their structure.

Contribution

It introduces a factorization method for 3-fold flips and contractions to curves using a sequence of elementary birational transformations.

Findings

Factorization of flips and contractions into basic steps

Application of weighted blow-ups and flops in the process

Simplification of complex 3-fold transformations

Abstract

We show that 3-fold terminal flips and divisorial contractions to a curve may be factored by a sequence of weighted blow-ups, flops, blow-downs to a locally complete intersection curve in a smooth 3-fold or divisorial contractions to a point.