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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.
##### MSC:
 14P25 Topology of real algebraic varieties 14H50 Plane and space curves
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