Self-dual metrics and twenty-eight bitangents
| dc.creator | Honda, Nobuhiro | |
| dc.date | 2004-03-31 | |
| dc.date | 2006-04-19 | |
| dc.date.accessioned | 2026-07-07T06:36:04Z | |
| dc.date.available | 2026-07-07T06:36:04Z | |
| dc.description | We consider self-dual metrics on 3CP^2 of positive scalar curvature admitting a non-trivial Killing field, but which is not conformally isometric to LeBrun's metrics. Firstly, we determine defining equations of the twistor spaces of such self-dual metrics. Next we prove that conversely, the complex threefolds defined by the equations always become twistor spaces of self-dual metrics on 3CP^2 of the above kind. As a corollary, we determine a global structure of the moduli spaces of these self-dual metrics; namely we show that the moduli space is non-empty and isomorphic to R^3/G, where G is an involution of R^3 having one-dimensional fixed locus. Combined with works of LeBrun, this settles a moduli problem of self-dual metrics on 3CP^2 of positive scalar curvature admitting a non-trivial Killing field. In our proof, a key role is played by a classical result in algebraic geometry that a smooth plane quartic always possesses twenty-eight bitangents. | |
| dc.description | 71 pages. V2; errors corrected. V3; 15 figures added | |
| dc.identifier | https://arxiv.org/abs/math/0403528 | |
| dc.identifier | http://arxiv.org/abs/math/0403528 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99974 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53C25; 14C05 | |
| dc.title | Self-dual metrics and twenty-eight bitangents | |
| dc.type | text |