Di Lorenzo, Alessio;
(2024)
Asymptotically conical Calabi-Yau conifolds.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
In this thesis we construct Ricci-flat metrics on asymptotically conical Calabi–Yau manifolds with isolated canonical singularities. These metrics will have two end behaviours: on one side, there is a complete asymptotically conical end, and on the other side there is one or more incomplete ends with polynomial decay to the conical Calabi–Yau metrics of the model cones at the singularities. This will be done by employing analysis on weighted Hölder spaces and techniques of Gromov– Hausdorff convergence on non-compact spaces, linking metric geometry with algebraic geometry. As an application, we will employ a gluing construction to prove the existence of special Lagrangian n-spheres vanishing cycles for smoothings in a small enough neighbourhood in the space of versal deformations of an asymptotically conical Calabi–Yau conifold with only nodal singularities.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Asymptotically conical Calabi-Yau conifolds |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. 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 Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > UCL School of Management |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10189058 |
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