Skip to main content Accessibility help
×
Home

Osculating hyperplanes and a quartic combinant of the nonsingular model of the Kummer and Weddle surfaces

  • R. H. Dye (a1)

Extract

The nonsingular model of Kummer's surface, or its birational equivalent the Weddle surface, is an octavic surface F in [5], projective space of dimension 5 (11), ((10), p. 53), ((1), pp. 218, 219). F is the base variety of a net N of quadrics with a common self-polar simplex S, and has on it 32 lines. These form a single orbit under the group G, of order 32, consisting of the harmonic homologies fixing S.

Copyright

References

Hide All
(1)Baker, H. F.Principles of geometry, vol IV (Cambridge University Press, 1925).
(2)Clebsch, A.Zur Theorie der binären Formen sechster Ordnung und zur Dreitheilung der hyperelliptschen Funktionen. Abh. Akad. Ges. der Wiss. zu Göttingen 14 (1869), 159.
(3)Dye, R. H.Osculating primes to curves of intersection in 4-space, and to certain curves in n-space. Proc. Edinburgh Math. Soc. 18 (Series II) (1972), 325338.
(4)Dye, R. H.The hyperosculating spaces to certain curves in [n]. Proc. Edinburgh Math. Soc. 19 (Series II) (1975), 301309.
(5)Dye, R. H.Pencils of elliptic quartics and an identification of Todd's quartic combinant. Proc. London Math. Soc. (3) 34 1977), 459478.
(6)Edge, W. L.Baker's property of the Weddle surface. J. London Math. Soc. 32 (1957), 463466.
(7)Edge, W. L.A new look at the Kummer surface. Canad. J. Math. 19 (1967), 952967.
(8)Edge, W. L.The osculating spaces of a certain curve in [n]. Proc. Edinburgh Math. Soc. 19 (Series II) (1974), 3944.
(9)Edge, W. L.Non-singular models of specialized Weddle surfaces. Math. Proc. Cambridge Phil. Soc. 80 (1976), 399418.
(10)Hudson, R. W. H. T.Kummer's quartic surface (Cambridge University Press, 1905).
(11)Klein, F.Zur Theorie der Linienkomplexe des ersten und zweiten Grades. Math. Ann. 2 (1870), 198226.
(12)Room, T. G.The geometry of determinantal loci (Cambridge University Press, 1938).
(13)Segre, C. Encyklopädie der Mathematischen Wissensehaften. III. Geometric, Leipzig, 1912.
(14)Semple, J. G. and Roth, L.An introduction to algebraic geometry (Clarendon Press, Oxford, 1949).
(15)Semple, J. G. and Kneebone, G. T.Algebraic curves (Clarendon Press, Oxford, 1959).
(16)Tyrrell, J. A.Degenerate plane cubics and a theorem of Clebsch. Bull. London Math. Soc. 5 (1973), 203208.
(17)Walker, R. J.Algebraic curves (Princeton University Press, 1950).

Osculating hyperplanes and a quartic combinant of the nonsingular model of the Kummer and Weddle surfaces

  • R. H. Dye (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.