Algebraic and Analytic K-Stability
| dc.creator | Paul, Sean T. | |
| dc.creator | Tian, Gang | |
| dc.date | 2004-05-27 | |
| dc.date.accessioned | 2026-07-07T05:08:39Z | |
| dc.date.available | 2026-07-07T05:08:39Z | |
| dc.description | In this note we identify the leading terms of the (reduced) K-energy map with a universal linear combination of the principal and subdominant coefficients of the weight of the $mth$ Hilbert point. This shows that the weight $F_{1}(λ;X)$ introduced by Donaldson in [SKD02] is just the weight of the CM-polarisation.The equivalence between the CM-(semi)stability and the K-(semi) stability follows from this. Also, using our previous work, we are able to describe this subdominant coefficient in terms of the weights of some generalised Chow forms, under a multiplicity free hypothesis on the degeneration. This is accomplished by introducing a parameter dependent lift of the CM-polarisation, and letting this parameter tend to infinity. This could be thought of as a ``quantized'' version of the virtual bundle introduced in [Tian94]. | |
| dc.identifier | https://arxiv.org/abs/math/0405530 | |
| dc.identifier | http://arxiv.org/abs/math/0405530 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71350 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.title | Algebraic and Analytic K-Stability | |
| dc.type | text |