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Harnack's curve theorem

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Harnack's curve theorem

number of connected components an algebraic curve can have

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About Harnack's curve theorem

In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, gives the possible numbers of connected components that an algebraic curve can have, in terms of the degree of the curve. For any algebraic curve of degree m in the real projective plane, the number of components c is bounded by

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Facts from Wikidata (CC0).