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An inequality for the number of nonempty ovals of a curve of odd degree. (English. Russian original) Zbl 0793.14021
St. Petersbg. Math. J. 4, No. 3, 539-548 (1993); translation from Algebra Anal. 4, No. 3, 159-170 (1992).
Summary: The authors prove restrictions on the topology of real nonsingular plane projective algebraic curves of odd degree, formulated by V. A. Rokhlin in Russ. Math. Surv. 33, 85-98 (1978); translation from Usp. Mat. Nauk 33, No. 5(203), 77-89 (1978; Zbl 0437.14013), and by O. Ya. Viro in Russ. Math. Surv. 41, No. 3, 55-82 (1986); translation from Usp. Mat. Nauk 41, No. 3(249), 45-67 (1986; Zbl 0619.14015), theorems 3.10 and 3.11. In the proof an essential role is played by results about homology of branched coverings, which are of independent interest: the authors indicate a homological construction that connects the homology class of a cyclic branched covering, constructed from a membrane, which is stretched on the base, and the homology class of the boundary of this membrane in a submanifold of the branching.
MSC:
14H45 Special algebraic curves and curves of low genus
14P25 Topology of real algebraic varieties
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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