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- Stable_curve abstract "In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory. This is equivalent to the condition that it is a complete connected curve whose only singularities are ordinary double points and whose automorphism group is finite. The condition that the automorphism group is finite can be replaced by the condition that it is not of arithmetic genus one and every non-singular rational component meets the other components in at least 3 points (Deligne & Mumford 1969). A semi-stable curve is one satisfying similar conditions, except that the automorphism group is allowed to be reductive rather than finite (or equivalently its connected component may be a torus). Alternatively the condition that non-singular rational components meet the other components in at least 3 points is replaced by the condition that they meet in at least 2 points. Similarly a curve with a finite number of marked points is called stable if it is complete, connected, has only ordinary double points as singularities, and has finite automorphism group. For example an elliptic curve (a non-singular genus 1 curve with 1 marked point) is stable.Over the complex numbers, a connected curve is stable if and only if, after removing all singular and marked points, the universal covers of all its components are isomorphic to the unit disk.".
- Stable_curve wikiPageExternalLink item?id=PMIHES_1969__36__75_0.
- Stable_curve wikiPageID "18948788".
- Stable_curve wikiPageRevisionID "603891573".
- Stable_curve hasPhotoCollection Stable_curve.
- Stable_curve subject Category:Algebraic_curves.
- Stable_curve subject Category:Moduli_theory.
- Stable_curve type Abstraction100002137.
- Stable_curve type AlgebraicCurves.
- Stable_curve type Attribute100024264.
- Stable_curve type Curve113867641.
- Stable_curve type Line113863771.
- Stable_curve type Shape100027807.
- Stable_curve comment "In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory. This is equivalent to the condition that it is a complete connected curve whose only singularities are ordinary double points and whose automorphism group is finite.".
- Stable_curve label "Courbe stable".
- Stable_curve label "Stable curve".
- Stable_curve sameAs Courbe_stable.
- Stable_curve sameAs m.04jk9mb.
- Stable_curve sameAs Q3001219.
- Stable_curve sameAs Q3001219.
- Stable_curve sameAs Stable_curve.
- Stable_curve wasDerivedFrom Stable_curve?oldid=603891573.
- Stable_curve isPrimaryTopicOf Stable_curve.