Abstract
We prove that mirror nonsingular configurations of m points and n lines in ℝP 3 exist only for m≤3, n≡0 or 1 (mod 4) and for m=0 or 1 (mod 4), n≡0 (mod 2). In addition, we give an elementary proof of V. M. Kharlamov’s well-known result saying that if a nonsingular surface of degree four in ℝP 3 is noncontractible and has M≥5 components, then it is nonmirror. For the cases M=5, 6, 7 and 8, Kharlamov suggested an elementary proof using an analogy between such surfaces and configurations of M−1 points and a line. Our proof covers the remaining cases M=9, 10. Bibliography: 5 titles.
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References
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 299–308.
Translated by N. Yu. Netsvetaev.
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Podkorytov, S.S. Mirror configurations of points and lines and algebraic surfaces of degree four. J Math Sci 91, 3526–3531 (1998). https://doi.org/10.1007/BF02434931
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DOI: https://doi.org/10.1007/BF02434931