Homological projective duality for Sym^2 P^n


In 2011, Hosono and Takagi constructed an interesting example of two derived equivalent, non-birational Calabi-Yau 3-folds. This example can be explained by phrasing it in terms of Kuznetsov’s theory of homological projective duality. With this as motivation, we compute the homological projective dual of Sym^2 P^n, and by taking n = 4 we recover Hosono and Takagi’s example. I will explain this result and its proof, which showcases a general technique for approaching HP duality, based on “gauged LG models and variation of GIT stability”.