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Title: The homological projective dual of Sym² P(V)
Author: Rennemo, Jørgen Vold
ISNI:       0000 0004 6348 1155
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2015
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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.
Supervisor: Thomas, Richard Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral