Gushchin, M. A.; Korobeinikov, A. N.; Polotovskij, G. M. 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 Keywords:construction of decomposable curves; \(M\)-cubic; \(M\)-quartic Citations:Zbl 0826.14032; Zbl 0605.14021 PDFBibTeX XMLCite \textit{M. A. Gushchin} et al., J. Math. Sci., New York 113, No. 6, 795--803 (2000; Zbl 1027.14031); translation from Zap. Nauchn. Semin. POMI 267, 119--132 (2000) Full Text: DOI