Homogeneous deformations of toric pairs

TL;DR

This paper extends the construction of homogeneous deformations from affine toric varieties to toric pairs, including boundary divisors, and applies it to generalize results on Fano toric pairs.

Contribution

It introduces a new method for deforming toric pairs, broadening the scope of previous deformation techniques for affine toric varieties.

Findings

Generalized deformation construction for toric pairs

Extended Ilten's result to Fano toric pairs

Provided new tools for studying toric boundary deformations

Abstract

We extend the Altmann--Mavlyutov construction of homogeneous deformations of affine toric varieties to the case of toric pairs $(X, \partial X)$, where $X$ is an affine or projective toric variety and $\partial X$ is its toric boundary. As an application, we generalise a result due to Ilten to the case of Fano toric pairs.