Resolution of singularities for a family of third-order differential systems with small meromorphic solution spaces

Details Resolution of singularities for a family of third-order differential systems with small meromorphic solution spaces Resolution of singularities for a family of third-order differential systems with small meromorphic solution spaces

2005-05-11

arxiv.org/abs/math/0505201v1

Kyushu J. Math. Vol. 59,2005,pp.307-320

Mathematics

Algebraic Geometry

11 pages, 4 figures

Scientific paper

Regarding the resolution of singularities for the differential equations of Painlev\'e type, there are important differences between the second-order Painlev\'e equations and those of higher order. Unlike the second-order case, in higher order cases there may exist some meromorphic solution spaces with codimension 2. In this paper, we will give an explicit global resolution of singularities for a 3-parameter family of third-order differential systems with meromorphic solution spaces of codimension 2.

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