Generalized Donaldson-Thomas invariants via kirwan blowups
Abstract/Contents
- Abstract
- In this thesis, we develop a virtual cycle approach towards generalized Donaldson-Thomas theory of Calabi-Yau threefolds. Starting with an Artin moduli stack parametrizing semistable sheaves or perfect complexes, we construct an associated Deligne-Mumford stack, called its Kirwan partial desingularization, with an induced semi-perfect obstruction theory of virtual dimension zero, and define the generalized Donaldson-Thomas invariant via Kirwan blowups as the degree of the corresponding virtual cycle. The key ingredients are a generalization of Kirwan's partial desingularization procedure and recent results from derived symplectic geometry regarding the local structure of stacks of sheaves and perfect complexes on Calabi-Yau threefolds. Examples of applications include Gieseker stability of coherent sheaves and Bridgeland and polynomial stability of perfect complexes. In the case of Gieseker semistable sheaves, this new Donaldson-Thomas invariant is invariant under deformations of the complex structure of the Calabi-Yau threefold. More generally, deformation invariance is true under appropriate assumptions which are expected to hold in all cases.
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 | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Savvas, Michail |
|---|---|
| Degree supervisor | Li, Jun, (Mathematician) |
| Thesis advisor | Li, Jun, (Mathematician) |
| Thesis advisor | Kemeny, Michael |
| Thesis advisor | Vakil, Ravi |
| Degree committee member | Kemeny, Michael |
| Degree committee member | Vakil, Ravi |
| Associated with | Stanford University, Department of Mathematics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Michail Savvas. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Michail Savvas
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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