Doyle, Bradley Roualeyn;
(2021)
Homological Projective Duality for the Plücker embedding of the Grassmannian.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
We describe the Kuznetsov component of the Plücker embedding of the Grassmannian as a category of matrix factorizations on an noncommutative crepant resolution (NCCR) of the affine cone of the Grassmannian. We also extend this to a full homological projective dual (HPD) statement for the Plücker embedding. The first part is finding and describing the NCCR, which is also of independent interest. We extend results of Špenko and Van den Bergh to prove the existence of an NCCR for the affine cone of the Grassmannian. We then relate this NCCR to a categorical resolution of Kuznetsov. Deforming these categories to categories of matrix factorizations we find the connection to the Kuznetsov component of the Grassmannian via Knörrer periodicity. In the process we prove a derived equivalence between two different NCCR's, this shows Hori duality for the group SL. Finally we put this all into the HPD framework.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Homological Projective Duality for the Plücker embedding of the Grassmannian |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2021. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10136764 |
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