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

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.