Towards Homological Projective duality for S^2 P^3 and S^2 P^4

TL;DR

This paper develops homological methods to explore conjectural dualities between certain symmetric square projective spaces and specific double covers branched along determinantal loci, advancing the understanding of homological projective duality.

Contribution

It establishes the homological foundations for conjectural dualities involving S^2 P^3 and S^2 P^4 with particular double covers branched along determinantal varieties.

Findings

Homological foundations for dualities between S^2 P^3 and a branched double cover.

Homological foundations for dualities between S^2 P^4 and a symmetric determinantal quintic.

Progress towards proving conjectural homological projective dualities.

Abstract

We provide homological foundations to establish conjectural homological projective dualities between 1) S^2 P^3 and the double cover of the projective 9-space branched along the symmetric determinantal quartic, and 2) S^2 P^4 and the double cover of the symmetric determinantal quintic in the projective 14-space branched along the symmetric determinantal locus of rank at most 3.