Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Shinobu Hosono, Hiromichi Takagi
We provide homological foundations to establish conjectural homological projective dualities in two cases; 1) the duality between ${\mathsf{S}}^2{\mathbb{P}}^3$ and the double cover of the projective 9-space branched along the symmetric determinantal quartic, and 2) the duality between ${\mathsf{S}}^2{\mathbb{P}}^4$ and the double cover of the symmetric determinantal quintic in ${\mathbb{P}}^{14}$ branched along the symmetric determinantal locus of rank at most 3.