Geometric transitions between Calabi-Yau threefolds related to Kustin-Miller unprojections

TL;DR

This paper explores geometric transitions between Calabi-Yau threefolds via Kustin-Miller unprojections, connecting various families and providing explicit equations, including two new examples with Picard rank one.

Contribution

It introduces new Calabi-Yau threefold examples and clarifies the role of Kustin-Miller unprojections in geometric transitions.

Findings

Connected many Calabi-Yau families through unprojections

Explicit equations for known Calabi-Yau families

Discovered two new Calabi-Yau threefolds with Picard rank one

Abstract

We study Kustin-Miller unprojections between Calabi-Yau threefolds or more precisely the geometric transitions they induce. We use them to connect many families of Calabi-Yau threefolds with Picard number one to the web of Calabi Yau complete intersections. This enables us to find explicit description of a few known families of Calabi-Yau threefolds in terms of equations. Moreover we find two new examples of Calabi-Yau threefolds with Picard group of rank one, described by Pfaffian equations in weighted projective spaces.