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Thesis

Universal D-modules, and factorisation structures on Hilbert schemes of points

Abstract:

This thesis concerns the study of chiral algebras over schemes of arbitrary dimension 𝑛.

In Chapter I, we construct a chiral algebra over each smooth variety 𝑋 of dimension 𝑛. We do this via the Hilbert scheme of points of 𝑋, which we use to build a factorisation space over 𝑋. Linearising this space produces a factorisation algebra over 𝑋, and hence, by Koszul duality, the desired chiral algebra. We begin the chapter with an overview of the theory of factorisation and chiral a...

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Department:
Mathematical Institute, University of Oxford
Role:
Supervisor
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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