THE HYPERGEOMETRIC DIFFERENTIAL EQUATION 3E2 WITH CUBIC CURVES AS SCHWARZ IMAGES
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概要
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Let 3E2(a1,a2,a3;b1,b2) denote the generalized hypergeometric differential equation of rank three with parameters (a1,a2,a3,b1,b2), which is defined on the projective line P1(x) with regular singularities at x =0, 1, ∞. Any set of linearly independent solutions defines a multi-valued map from P1 -{0, 1, ∞}to the projective plane P2 called the Schwarz map. The image of this map is locally a curve, determined uniquely up to projective transformations. The condition for the image curve to be a cubic curve is written in terms of the parameters, and we list those curves and study the action of the monodromy groups on them.
著者
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Kato Mitsuo
Department Of Mathematics College Of Education University Of The Ryukyus
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Sasaki Takeshi
Department Of Agricultural Chemistry Faculty Of Agriculture Ehime University
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