Local cohomology of generalized Okamoto-Painlevé pairs and Painlevé equations

dc.creatorTerajima, Hitomi
dc.date2000-06-05
dc.date.accessioned2026-07-07T04:35:42Z
dc.date.available2026-07-07T04:35:42Z
dc.descriptionIn 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.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0006027
dc.identifierhttp://arxiv.org/abs/math/0006027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59345
dc.subjectAlgebraic Geometry
dc.subject14D15;14J26;32G10;34M55
dc.titleLocal cohomology of generalized Okamoto-Painlevé pairs and Painlevé equations
dc.typetext

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