Abstract
Given h,k≥0, M(h,k) denotes the set of nonsingular mixed configurations of h lines and k points in ℝ3. We will say that f∈M(h,k) is mirror if it is isotopic to its mirror image in any plane. The following problem has been proposed by Viro and Drobotukhina [3]: given h,k≥0, does there exist some mirror configuration on M(h,k)? A satisfactory answer is given when h=1: f∈M(1,k) is mirror if and only if k≤3.
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Bibliography
V. M. Kharlamov, Non-amphicheiral surfaces of degree 4 in ℝP3, Topology and Geometry (Rokhlin Seminar), Lecture Notes in Math., vol.1346, Springer, 1988, pp. 349–356.
O. Ya. Viro, Topological problems concerning lines and points of three-dimensional space, Soviet Math. Dokl. 32 (1985), no.2, pp. 528–531.
O. Ya. Viro and Yu. V. Drobotukhina, Configurations of skew lines, Leningrad Math. J. 1 (1990), no.4, pp. 1027–1050.
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© 1992 Springer-Verlag
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Borobia, A. (1992). Mirror property for nonsingular mixed configurations of one line and k points in R3 . In: Coste, M., Mahé, L., Roy, MF. (eds) Real Algebraic Geometry. Lecture Notes in Mathematics, vol 1524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084614
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DOI: https://doi.org/10.1007/BFb0084614
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