Calabi--Yau threefolds in $\mathbb{P}^6$

TL;DR

This paper classifies certain Calabi--Yau threefolds in six-dimensional projective space, focusing on quasi-Buchsbaum varieties, and includes those in singular quadrics and of degree up to 14.

Contribution

It provides a complete classification of quasi-Buchsbaum Calabi--Yau threefolds in $P^6$, expanding understanding of their geometric properties and embeddings.

Findings

Classified all quasi-Buchsbaum Calabi--Yau threefolds in $P^6$

Included all Calabi--Yau threefolds in singular 5-dimensional quadrics

Identified all Calabi--Yau threefolds of degree ≤ 14 in $P^6$

Abstract

We study the geometry of $3$-codimensional smooth subvarieties of the complex projective space. In particular, we classify all quasi-Buchsbaum Calabi--Yau threefolds in projective $6$-space. Moreover, we prove that this classification includes all Calabi--Yau threefolds contained in a possibly singular 5-dimensional quadric as well as all Calabi--Yau threefolds of degree at most $14$ in $\mathbb{P}^6$.