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

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 result 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, which are described by Pfaffian equations in weighted projective spaces.