Title: On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations,
Abstract: We study quartic double fivefolds from the perspective of Fano manifolds of
Calabi-Yau type and that of exceptional quaternionic representations. We first
prove that the generic quartic double fivefold can be represented, in a finite
number of ways, as a double cover of P^5 ramified along a linear section of the
Sp 12-invariant quartic in P^31. Then, using the geometry of the Vinberg's type
II decomposition of some exceptional quaternionic representations, and backed
by some cohomological computations performed by Macaulay2, we prove the
existence of a spherical rank 6 vector bundle on such a generic quartic double
fivefold. We finally use the existence this vector bundle to prove that the
homological unit of the CY-3 category associated by Kuznetsov to the derived
category of a generic quartic double fivefold is C $\oplus$ C[3].