Factoring threefold divisorial contractions to points

TL;DR

This paper demonstrates that complex threefold divisorial contractions to points with higher index can be decomposed into simpler operations like flips, flops, and minimal discrepancy contractions, aiding understanding of their structure.

Contribution

It introduces a method to factor certain threefold divisorial contractions into elementary steps, advancing the classification of these contractions.

Findings

Factorization into flips, flops, and minimal discrepancy contractions.

Applicable to contractions with non-minimal discrepancy and index > 1.

Enhances understanding of threefold divisorial contractions.

Abstract

We show that terminal 3-fold divisorial contraction to a point of index $>1$ with non-minimal discrepancy may be factored into a sequence of flips, flops and divisorial contractions to a point with minimal discrepancies.