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Patchworking arrangements of a cubic and a quartic. (English. Russian original) Zbl 1027.14031
J. Math. Sci., New York 113, No. 6, 795-803 (2003); translation from Zap. Nauchn. Semin. POMI 267, 119-132 (2000).
Summary: B. Sturmfels [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 21, 377-386 (1994; Zbl 0826.14032)] modified Viro’s “patchworking” [O. Ya. Viro in: Topology Conf., Proc., Collect. Rep., Leningrad 1982, 149-197 (1983; Zbl 0605.14021)] method and applied it for construction of complete intersections. In the paper, this modification is used for construction of decomposable curves. 11 new arrangements of an \(M\)-cubic and an \(M\)-quartic with 12 common points lying on the odd branch of the cubic and an oval of the quartic are realized.
14P25 Topology of real algebraic varieties
14H50 Plane and space curves
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