Properties of moderate toric resolutions in dimension three

TL;DR

This paper investigates the properties and existence of moderate toric resolutions in three-dimensional algebraic geometry, focusing on their relation to F-blowups, essential divisors, and Hilbert basis resolutions.

Contribution

It provides new insights into the existence and properties of moderate toric resolutions in dimension three, connecting them with birational geometry and Hilbert basis resolutions.

Findings

Characterizes conditions for the existence of moderate toric resolutions.

Analyzes properties of these resolutions in relation to F-blowups.

Explores implications for birational geometry and essential divisors.

Abstract

We study moderate toric resolutions introduced by Ch\'avez-Mart\'inez, Duarte and Yasuda, which appears in the relation between F-blowups and essential divisors. In particular, we address the problems, when it exists, and if it is the case, what properties it has in conjunction with the birational geometry and Hilbert basis resolutions, mainly in dimension three.