Nodal curves and Riccati solutions of Painlevé equations
| dc.creator | Saito, Masa-Hiko | |
| dc.creator | Terajima, Hitomi | |
| dc.date | 2002-01-23 | |
| dc.date.accessioned | 2026-07-07T04:46:04Z | |
| dc.date.available | 2026-07-07T04:46:04Z | |
| dc.description | In this paper, we study Riccati solutions of Painlevé equations from a view point of geometry of Okamoto-Painlevé pairs $(S,Y)$. After establishing the correspondence between (rational) nodal curves on $S-Y$ and Riccati solutions, we give the complete classification of the configurations of nodal curves on $S-Y$ for each Okamoto-Painlevé pair $(S, Y)$. As an application of the classification, we prove the non-existence of Riccati solutions of Painlevé equations of types $P_{I}, P_{III}^{\tilde{D}_8}$ and $P_{III}^{\tilde{D}_7}$. We will also give a partial answer to the conjecture in (STT) and (T) that the dimension of the local cohomology $H^1_{Y_{red}}(S,Θ_S(-\log Y_{red}))$ is one. | |
| dc.description | 30 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0201225 | |
| dc.identifier | http://arxiv.org/abs/math/0201225 | |
| dc.identifier | J. Math. Kyoto Univ., 44(2004), no.3, 529--568 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63187 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Quantum Algebra | |
| dc.subject | 14D15, 34M55, 32G10 | |
| dc.title | Nodal curves and Riccati solutions of Painlevé equations | |
| dc.type | text |