# Some examples of Calabi-Yau pairs with maximal intersection and no toric model

## TL;DR

This paper presents examples of Calabi-Yau pairs with maximal intersection that cannot be modeled torically, highlighting differences from the surface case and expanding understanding of higher-dimensional Calabi-Yau geometry.

## Contribution

It provides the first known examples of higher-dimensional Calabi-Yau pairs with maximal intersection that lack a toric model, contrasting with the surface case.

## Key findings

- Existence of Calabi-Yau pairs with no toric model in higher dimensions
- Maximal intersection does not imply toric representability in higher dimensions
- Examples challenge assumptions based on surface case behavior

## Abstract

It is known that a maximal intersection log canonical Calabi-Yau surface pair is crepant birational to a toric pair. This does not hold in higher dimension: this paper presents some examples of maximal intersection Calabi-Yau pairs that admit no toric model.