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- Harnack's_curve_theorem abstract "In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, describes 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 byThe maximum number is one more than the maximum genus of a curve of degree m, attained when the curve is nonsingular. Moreover, any number of components in this range of possible values can be attained. A curve which attains the maximum number of real components is called an M-curve (from "maximum") – for example, an elliptic curve with two components, such as or the Trott curve, a quartic with four components, are examples of M-curves.This theorem formed the background to Hilbert's sixteenth problem.".
- Harnack's_curve_theorem thumbnail ECClines-3.svg?width=300.
- Harnack's_curve_theorem wikiPageID "5209604".
- Harnack's_curve_theorem wikiPageRevisionID "461636590".
- Harnack's_curve_theorem hasPhotoCollection Harnack's_curve_theorem.
- Harnack's_curve_theorem subject Category:Real_algebraic_geometry.
- Harnack's_curve_theorem subject Category:Theorems_in_algebraic_geometry.
- Harnack's_curve_theorem type Abstraction100002137.
- Harnack's_curve_theorem type Communication100033020.
- Harnack's_curve_theorem type Message106598915.
- Harnack's_curve_theorem type Proposition106750804.
- Harnack's_curve_theorem type Statement106722453.
- Harnack's_curve_theorem type Theorem106752293.
- Harnack's_curve_theorem type TheoremsInAlgebraicGeometry.
- Harnack's_curve_theorem comment "In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, describes 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 byThe maximum number is one more than the maximum genus of a curve of degree m, attained when the curve is nonsingular.".
- Harnack's_curve_theorem label "Harnack's curve theorem".
- Harnack's_curve_theorem sameAs m.0d7zmp.
- Harnack's_curve_theorem sameAs Q5659675.
- Harnack's_curve_theorem sameAs Q5659675.
- Harnack's_curve_theorem sameAs Harnack's_curve_theorem.
- Harnack's_curve_theorem wasDerivedFrom Harnack's_curve_theorem?oldid=461636590.
- Harnack's_curve_theorem depiction ECClines-3.svg.
- Harnack's_curve_theorem isPrimaryTopicOf Harnack's_curve_theorem.
