Nash modification on toric curves

TL;DR

This paper investigates the process of resolving singularities in toric curves using Nash modification, providing bounds on iteration counts and introducing a new combinatorial approach to improve understanding and efficiency.

Contribution

It offers a new bound on the number of Nash modification iterations needed for resolution and introduces a novel combinatorial division algorithm approach.

Findings

Bound on the number of Nash iterations for resolution

A new combinatorial division algorithm for Nash modification

Enhanced understanding of the resolution process for toric curves

Abstract

We revisit the problem of resolution of singularities of toric curves by iterating Nash modification. We give a bound on the number of iterations required to obtain the resolution. We also introduce a different approach on counting iterations by dividing the combinatorial algorithm of Nash modification of toric curves into several division algorithms.