抄録
Abstract. In the theory of deformation of Okamoto-Painleve pair (S, Y), a local cohomology group H1D (_??_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 H1D (_??_s (-log D)) is at least 1 dimensional. This fact is the key for understanding Painlevé equation related to (S, Y). Moreover we show that, for the pairs (S, Y) of type Ã8, the local cohomology group H1D (_??_S (-log D)) vanishes. Therefore in this case, there is no differential equation on S-Y in the sense of the theory.
