Double spinor Calabi-Yau varieties

TL;DR

This paper studies special Calabi-Yau fivefolds arising from intersections of spinor varieties and their duals, proving their derived and L-equivalence despite not being birationally equivalent.

Contribution

It demonstrates derived and L-equivalence of two Calabi-Yau fivefolds constructed from spinor varieties, revealing new relationships in algebraic geometry.

Findings

X and Y are smooth Calabi-Yau fivefolds.

X and Y are not birationally equivalent.

X and Y are derived and L-equivalent.

Abstract

Consider the ten-dimensional spinor variety in the projectivization of a half-spin representation of dimension sixteen. The intersection X of two general translates of this variety is a smooth Calabi-Yau fivefold, as well as the intersection Y of their projective duals. We prove that although X and Y are not birationally equivalent, they are derived equivalent and L-equivalent in the sense of Kuznetsov and Shinder.