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Riemann existence theorem and construction of real algebraic curves. (English) Zbl 1078.14083
Using the Riemann existence theorem, the author shows the existence of certain real rational maps \(f\) that are of the form \(D/q^2\), where \(D=4p^3+27q^2\). The author then studies the topology of the real algebraic curve defined by the equation \(y^3+p(x)y+q(x)=0\), and proves the existence of some new topological types of real algebraic curves on real Hirzebruch surfaces.

MSC:
14P05 Real algebraic sets
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