  We study the derived category of a complete intersection X of bilinear
divisors in the orbifold Sym^2 P(V). Our results are in the spirit of
Kuznetsov's theory of homological projective duality, and we describe a
homological projective duality relation between Sym^2 P(V) and a category of
modules over a sheaf of Clifford algebras on P(Sym^2 V^vee).
  The proof follows a recently developed strategy combining variation of GIT
stability and categories of global matrix factorisations. We begin by
translating D^b(X) into a derived category of factorisations on an LG model,
and then apply VGIT to obtain a birational LG model. Finally, we interpret the
derived factorisation category of the new LG model as a Clifford module
category.
  In some cases we can compute this Clifford module category as the derived
category of a variety. As a corollary we get a new proof of a result of Hosono
and Takagi, which says that a certain pair of nonbirational Calabi-Yau 3-folds
have equivalent derived categories.

Algebraic Geometry