An algorithm for the minimal model program in dimension three

TL;DR

This paper presents an algorithm for executing the minimal model program in three dimensions over algebraic number fields, along with auxiliary algorithms for related algebraic computations.

Contribution

It introduces a novel algorithm for the minimal model program in dimension three and auxiliary algorithms for computing Hom modules and Stein factorizations.

Findings

Successfully constructs the minimal model program algorithm in dimension three.

Provides algorithms for computing bigraded global Hom modules.

Includes an algorithm for Stein factorization.

Abstract

We construct an algorithm for the minimal model program in dimension three over the field of algebraic numbers. As auxiliary results, we also construct algorithms for computing bigraded global Hom modules and for computing Stein factorization.