
TL;DR
This paper demonstrates that complex birational transformations of 3-dimensional algebraic varieties can be decomposed into simpler, well-understood operations such as flops, blow-downs, and divisorial contractions, aiding classification efforts.
Contribution
It introduces a factorization approach for 3-fold terminal flips and contractions into elementary steps, advancing the understanding of their structure.
Findings
3-fold terminal flips can be factored into flops and contractions.
Divisorial contractions to points with minimal discrepancies are included in the factorization.
The approach simplifies the analysis of 3-fold birational maps.
Abstract
We show that 3-fold terminal flips and divisorial contractions may be factored into a sequence of flops, blow-downs to a smooth curve in a smooth 3-fold or divisorial contractions to points with minimal discrepancies.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology
