Local cohomology of generalized Okamoto-Painlevé pairs and Painlevé equations
| dc.creator | Terajima, Hitomi | |
| dc.date | 2000-06-05 | |
| dc.date.accessioned | 2026-07-07T04:35:42Z | |
| dc.date.available | 2026-07-07T04:35:42Z | |
| dc.description | In the theory of deformation of Okamoto-Painlevé pair (S,Y), a local cohomology group $H^1_D(Θ_S(-\log D))$ plays an important role. In this paper, we estimate the local cohomology group of pair (S,Y) for several types, and obtain the following results. For a pair (S,Y) corresponding to the space of initial conditions of the Painlevé equations, we show that the local cohomology group $H^1_D(Θ_S(-\log D))$ is at least 1 dimensional. This fact is the key to understand Painlevé equation related to (S,Y). Moreover we show that, for the pairs (S,Y) of type $\tilde{A_8}$, the local cohomology group $H^1_D(Θ_S(-\log D))$ vanish. Therefore in this case, there is no differential equation on S-Y in the sense of the theory. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0006027 | |
| dc.identifier | http://arxiv.org/abs/math/0006027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59345 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D15;14J26;32G10;34M55 | |
| dc.title | Local cohomology of generalized Okamoto-Painlevé pairs and Painlevé equations | |
| dc.type | text |