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Caption: Mathematical Models by Arnold Emch - Series 4 (1928)
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34 Mathematical Models Fig. 21 A s has been pointed out before the study of these sextics is of considerable importance from the standpoint of geometry as well as that of function-theory, particularly the theory of Abelian functions in connection with an algebraic curve of genus four. T h e canonical series is in this case a g^\ = ge8 cut out by the linear system of cubics Xi 4 i + \ < > + X3<fe + \ < > = 0 through the six double-points. > 2/2 4/4 If w e set the four linearly independent adjoints < o equal to pji = f cr (x),i = 1, 2, 3, 4, the sextic in the plane is m a p p e d into a nonfi singular sextic Cq in S3 of genus four, which m a y be shown to be the intersection of a quadric and a cubic surface. T h e canonical series on Cq is n o w cut out by the planes. Xi^i + X2J2 + X3;y3 + X4^4 = 0. A m o n g the sextuples of the series those consisting of three couples of coincidences are of particular importance. Their number is obviously equal to the number of tritangent planes of Cq.
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