Deformations of log Calabi-Yau pairs can be obstructed

TL;DR

This paper presents examples of smooth projective varieties with anticanonical divisors where the deformations are obstructed, constructed using toric geometry, highlighting complexities in deformation theory of log Calabi-Yau pairs.

Contribution

It provides explicit examples of obstructed deformations of log Calabi-Yau pairs using toric geometry, advancing understanding of their deformation behavior.

Findings

Examples of obstructed deformations of $(X,D)$ pairs.

Construction of these examples via toric geometry.

Insights into deformation obstructions in log Calabi-Yau pairs.

Abstract

We exhibit examples of pairs $(X,D)$ where $X$ is a smooth projective variety and $D$ is an anticanonical reduced simple normal crossing divisor such that the deformations of $(X,D)$ are obstructed. These examples are constructed via toric geometry.