Algorithmic resolution via weighted blowings up

TL;DR

This paper presents a computer implementation of a weighted resolution algorithm for resolving singularities in characteristic zero, highlighting its efficiency and independence from historical data compared to previous methods.

Contribution

The authors implement and experimentally evaluate Abramovich, Temkin, and Wlodarczyk's weighted resolution algorithm, demonstrating its efficiency and distinct approach from traditional resolution algorithms.

Findings

Weighted resolution is remarkably efficient.

The implementation confirms independence from historical data.

Experimental comparison with Villamayor's algorithm shows improved performance.

Abstract

In this paper we describe a computer implementation of Abramovich, Temkin, and Wlodarczyk's algorithm for resolving singularities in characteristic zero. Their "weighted resolution" algorithm proceeds by repeatedly blowing up along centers that are independent of the history of the past blowing ups, distinguishing weighted resolution from previous resolution algorithms, which all rely on history. We compare our implementation of weighted resolution with that of Villamayor's resolution algorithm, experimentally verifying that weighted resolution is remarkably efficient.