The First Painleve Equation on the Weighted Projective Space
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چکیده
The first Painlevé equation is expressed as a vector field on the three dimensional weighted projective space CP (3, 2, 4, 5). With the aid of the dynamical systems theory and the orbifold structure of CP (3, 2, 4, 5), a simple proof of the Painlevé property and the construction of the space of initial conditions are given. In particular, Painlevé’s transformation is geometrically derived, which proves to be a Darboux coordinates of a certain algebraic surface with a holomorphic symplectic form.
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تاریخ انتشار 2013