Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712853 |
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Title: | The homological projective dual of Sym² P(V) | ||||||
Author: | Rennemo, Jørgen Vold |
ISNI:
0000 0004 6348 1155
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Awarding Body: | Imperial College London | ||||||
Current Institution: | Imperial College London | ||||||
Date of Award: | 2015 | ||||||
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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.
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Supervisor: | Thomas, Richard | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.712853 | DOI: | |||||
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