Towards homological projective duality for S2P3 and S2P4

We provide homological foundations to establish conjectural homological projective dualities in two cases; 1) the duality between S2P3 and the double cover of the projective 9-space branched along the symmetric determinantal quartic, and 2) the duality between S2P4 and the double cover of the symmetric determinantal quintic in P14 branched along the symmetric determinantal locus of rank at most 3.