The homological projective dual of Sym^2 P(V)
File(s)
Author(s)
Rennemo, Jørgen Vold
Type
Thesis
Abstract
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.
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.
Version
Open Access
Date Issued
2015-06
Date Awarded
2015-10
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Thomas, Richard
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)