On Calabi--Yau threefolds associated to a web of quadrics

TL;DR

This paper investigates the geometric relationship between a specific intersection of quadrics in seven-dimensional projective space containing a plane and a related double octic branched along a discriminant locus, revealing new insights into Calabi--Yau threefolds.

Contribution

It introduces a novel birational map connecting these complex geometric objects, expanding understanding of Calabi--Yau threefolds associated with webs of quadrics.

Findings

Established a birational equivalence between the intersection of quadrics and the double octic.

Described the geometric properties of the web of quadrics and its discriminant.

Provided new examples of Calabi--Yau threefolds related to webs of quadrics.

Abstract

We study the geometry of a birational map between an intersection of a web of quadrics in seven-dimensional complex projective space that contains a plane and the double octic branched along the discriminant of the web.