# Complete intersection Calabi--Yau threefolds in Hibi toric varieties and their smoothing

## TL;DR

This paper explores the combinatorial construction of Calabi-Yau threefolds within Hibi toric varieties, focusing on their singularities, smoothability, and topological invariants, with new examples illustrating these properties.

## Contribution

It provides a combinatorial framework for describing Calabi-Yau threefolds in Hibi toric varieties and analyzes their smoothing and topological invariants.

## Key findings

- Calabi-Yau threefolds in Hibi toric varieties often have conifold singularities.
- Many such threefolds are smoothable to non-singular Calabi-Yau threefolds.
- Explicit calculations of topological invariants for new examples are presented.

## Abstract

In this article, we summarize combinatorial description of complete intersection Calabi-Yau threefolds in Hibi toric varieties. Such Calabi-Yau threefolds have at worst conifold singularities, and are often smoothable to non-singular Calabi-Yau threefolds. We focus on such non-singular Calabi-Yau threefolds of Picard number one, and illustrate the calculation of topological invariants, using new motivating examples.