Pulling subdivisions of cones and blowups of monomial ideals on affine toric varieties

TL;DR

This paper addresses the problem of identifying an ideal whose blowup corresponds to a given map between normal toric varieties, specifically those arising from subdivisions of cones.

Contribution

It provides a method to explicitly find ideals associated with subdivisions of cones in the context of toric variety blowups.

Findings

Established a correspondence between cone subdivisions and ideals in toric varieties.

Provided an explicit construction for the ideal related to a given subdivision.

Solved the problem for maps of normal toric varieties induced by cone subdivisions.

Abstract

This short note solves the following problem: Given a map of normal toric varieties corresponding to a coherent subdivision of a cone, find an ideal such that the given map is the blowup of that ideal.