Double spinor Calabi-Yau varieties

Laurent Manivel (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: 14C34

Mots clés: Spinor variety; Calabi-Yau variety; derived equivalence; birational equivalence; projective duality; 14F05; 14J32; 14L35

Domaines: Géométrie algébrique [math.AG]

Laurent Manivel. Double spinor Calabi-Yau varieties. Épijournal de Géométrie Algébrique, 2019, 3, Article 2. ⟨hal-01583017v2⟩