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Gluing algebraic hypersurfaces, removing of singularities and constructions of curves. (Russian) Zbl 0605.14021
Topology conference, Proc., Collect. Rep., Leningrad 1982, 149-197 (1983).
This is dedicated to a detailed explanation of a new method of construction of real algebraic varieties with prescribed topological properties and of the publication of certain constructions realizable with their help. Especially there are constructed M-curves of degree 8 and counterexamples to the Ragsdale conjecture [V. Ragsdale, Am. J. Math. 28, 377-404 (1906)] which were announced by the author in Sov. Math. Dokl. 22, 566-570 (1980); translation from Dokl. Akad. Nauk SSSR 254, 1306-1310 (1980; Zbl 0581.14009). The assemblings are based on a construction which builds from some algebraic hypersurfaces a new one resulting in the topological point of view from gluing the origins.

MSC:
14Pxx Real algebraic and real-analytic geometry
14N05 Projective techniques in algebraic geometry
14F45 Topological properties in algebraic geometry
Citations:
Zbl 0581.14009