Toroidalization of Locally Toroidal Morphisms

TL;DR

This paper addresses the toroidalization problem for locally toroidal morphisms, providing a method to construct toroidal liftings through blow-ups in algebraic geometry.

Contribution

It offers a solution to the toroidalization problem specifically for locally toroidal morphisms, advancing the understanding of morphism modifications.

Findings

Provides a construction method for toroidal liftings

Solves the toroidalization problem in the locally toroidal case

Enhances techniques for morphism modifications in algebraic geometry

Abstract

The problem of toroidalization is to construct a toroidal lifting of a dominant morphism $\varphi:X\to Y$ of algebraic varieties by blowing up in the target and domain. This paper contains a solution to this problem when $\varphi$ is locally toroidal.