Kummer's Quartic Surface
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Similarly the tetrads of nodes 0, 45, 12, 63 and 35, 43, 46, 65 are connected by elliptic segments. Each tetrad forms a four-cornered piece of the surface having two elliptic faces and four hyperbolic edges. Each of one group-set is attached at two nodes to each of the other group-set.
Consider the degenerate case when one node is taken on the quadric 123.456. Of the harmonic conjugates of the real generators through with respect to the six pairs of direc- trices lying on the surface and named ...after them, only (12) of one system and (45) (56) (64) of the other system are real, since the correlations associated with a^ = 0, and x 2 = 0, separately, trans- form a real line into an imaginary one. Hence the nodes in this 124 REALITY AND TOPOLOGY [CH. XI degenerate case lie at the intersections of two and four generators, and this gives a diagram of their relative situation in the general case.
Hi IIP mm Fig. 16.
As in case I each piece is cut in pairs of points by three directrices; there is this difference to I a that each elliptic segment contains a point where the two inflexional tangents have four- point contact, but are imaginary.
What to read after Kummer's Quartic Surface?
You can find similar books in the "Read Also" column, or choose other free books by Baker, H. F. (Henry Frederick), 1866-1956 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Similarly the tetrads of nodes 0, 45, 12, 63 and 35, 43, 46, 65 are connected by elliptic segments. Each tetrad forms a four-cornered piece of the surface having two elliptic faces and four hyperbolic edges. Each of one group-set is attached at two nodes to each of the other group-set.
Consider the degenerate case when one node is taken on the quadric 123.456. Of the harmonic conjugates of the real generators through with respect to the six pairs of direc- trices lying on the surface and named ...after them, only (12) of one system and (45) (56) (64) of the other system are real, since the correlations associated with a^ = 0, and x 2 = 0, separately, trans- form a real line into an imaginary one. Hence the nodes in this 124 REALITY AND TOPOLOGY [CH. XI degenerate case lie at the intersections of two and four generators, and this gives a diagram of their relative situation in the general case.
Hi IIP mm Fig. 16.
As in case I each piece is cut in pairs of points by three directrices; there is this difference to I a that each elliptic segment contains a point where the two inflexional tangents have four- point contact, but are imaginary.
What to read after Kummer's Quartic Surface?
You can find similar books in the "Read Also" column, or choose other free books by Baker, H. F. (Henry Frederick), 1866-1956 to read onlineMoreLess
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