On Oda's Strong Factorization Conjecture

TL;DR

This paper presents an algorithmic approach to Oda's Strong Factorization Conjecture for smooth toric varieties, including reductions, simplifications, and proofs of special cases, advancing understanding of birational map decompositions.

Contribution

It introduces a new algorithm for constructing decompositions of birational maps and proves some special cases of the conjecture, providing progress towards its resolution.

Findings

Algorithm for factorization construction proposed

Reductions and simplifications of the algorithm developed

Special cases of the conjecture proved

Abstract

The Oda's Strong Factorization Conjecture states that a proper birational map between smooth toric varieties can be decomposed as a sequence of smooth toric blowups followed by a sequence of smooth toric blowdowns. This article describes an algorithm that conjecturally constructs such a decomposition. Several reductions and simplifications of the algorithm are presented and some special cases of the conjecture are proved.