Extremal metrics and K-stability (PhD thesis)
| dc.creator | Székelyhidi, Gábor | |
| dc.date | 2006-10-31 | |
| dc.date.accessioned | 2026-07-07T07:32:23Z | |
| dc.date.available | 2026-07-07T07:32:23Z | |
| dc.description | In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to be equivalent to the existence of an extremal metric in the polarisation class. A variant for a complete extremal metric on the complement of a smooth divisor is also given. On toric surfaces we prove a Jordan-Holder type theorem for decomposing semistable surfaces into stable pieces. On a ruled surface we compute the infimum of the Calabi functional for the unstable polarisations, exhibiting a decomposition analogous to the Harder-Narasimhan filtration of an unstable vector bundle. | |
| dc.description | 85 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611002 | |
| dc.identifier | http://arxiv.org/abs/math/0611002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119097 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53C55; 53C25 | |
| dc.title | Extremal metrics and K-stability (PhD thesis) | |
| dc.type | text |