Arithmetically Gorenstein Calabi-Yau threefolds in $\mathbb{P}^7$

TL;DR

This paper catalogs arithmetically Gorenstein Calabi-Yau threefolds in projective 7-space, introduces three new families, and provides evidence of their completeness, highlighting the lack of known mirror constructions.

Contribution

It presents a comprehensive list of such threefolds and constructs three new families, advancing the classification in algebraic geometry.

Findings

List of arithmetically Gorenstein Calabi-Yau threefolds in P^7

Construction of three new families

Evidence suggesting the list's completeness

Abstract

We present a list of arithmetically Gorenstein Calabi-Yau threefolds in $\mathbb{P}^7$ and give evidence that this is a complete list. In particular we construct three new families of arithmetically Gorenstein Calabi-Yau threefolds in $\mathbb{P}^7$ for which no mirror construction is known.