Gauge-theoretic invariants in algebraic geometry
Abstract/Contents
- Abstract
- In this thesis, we examine certain questions relevant to the study of sheaf-theoretic invariants of complex projective surfaces and beyond. In the first part, the virtual localization technique is applied to the problem of showing blow-up formulae for virtual invariants on a smooth projective surface by using the moduli spaces of m-stable sheaves in the sense of Nakajima and Yoshioka, who already proved analogous results for equivariant moduli spaces of framed sheaves on P2. This yields a very general blow-up formalism that is applied to prove a blowup formula for virtual Donaldson invariants. In the second part, the theory of the Atiyah class on algebraic stacks is developed. Here, several technical constructions are given. Some of these may have been known to experts but no suitable reference was found. The results provide the fundamental building blocks for the construction of perfect obstruction theories. They are used throughout the first part and may prove useful beyond this setting.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Kuhn, Nikolas Thomas Urs |
|---|---|
| Degree supervisor | Mazzeo, Rafe |
| Thesis advisor | Mazzeo, Rafe |
| Thesis advisor | Conrad, Brian, 1970- |
| Thesis advisor | Vakil, Ravi |
| Degree committee member | Conrad, Brian, 1970- |
| Degree committee member | Vakil, Ravi |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Nikolas Thomas Urs Kuhn. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/pg979xv3389 |
Access conditions
- Copyright
- © 2021 by Nikolas Thomas Urs Kuhn
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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