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In classical algebraic geometry, the genus–degree formula relates the degree d of an irreducible plane curve with its arithmetic genus g via the formula: Here "plane curve" means that is a closed curve in the projective plane . If the curve is non-singular the geometric genus and the arithmetic genus are equal, but if the curve is singular, with only ordinary singularities, the geometric genus is smaller. More precisely, an ordinary singularity of multiplicity r decreases the genus by .

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  • Genus–degree formula (en)
  • Formula genere-grado (it)
  • Formule genre-degré (fr)
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  • In classical algebraic geometry, the genus–degree formula relates the degree d of an irreducible plane curve with its arithmetic genus g via the formula: Here "plane curve" means that is a closed curve in the projective plane . If the curve is non-singular the geometric genus and the arithmetic genus are equal, but if the curve is singular, with only ordinary singularities, the geometric genus is smaller. More precisely, an ordinary singularity of multiplicity r decreases the genus by . (en)
  • En géométrie algébrique, la formule genre - degré est une équation reliant le degré d d'une courbe plane irréductible avec son genre arithmétique g par la formule : Ici « courbe plane » signifie que est une courbe fermée dans le plan projectif . Si la courbe est non singulière, le genre géométrique et le genre arithmétique sont égaux, mais si la courbe est singulière, avec seulement des singularités ordinaires, le genre géométrique a priori est plus petit. Plus précisément, une singularité ordinaire de multiplicité r diminue le genre de . (fr)
  • In matematica, e in particolare nella geometria algebrica classica, la formula genere-grado lega il grado di una curva piana che ammette solo singolarità ordinarie con il suo genere geometrico mediante la formula: dove è la molteplicità del punto della curva. Se la curva è non singolare, le molteplicità sono tutte uguali a e si ha la formula in tal caso il e il della curva coincidono. (it)
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  • Viktor S. (en)
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  • G/g043990 (en)
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  • Kulikov (en)
title
  • Genus of a curve (en)
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  • In classical algebraic geometry, the genus–degree formula relates the degree d of an irreducible plane curve with its arithmetic genus g via the formula: Here "plane curve" means that is a closed curve in the projective plane . If the curve is non-singular the geometric genus and the arithmetic genus are equal, but if the curve is singular, with only ordinary singularities, the geometric genus is smaller. More precisely, an ordinary singularity of multiplicity r decreases the genus by . (en)
  • En géométrie algébrique, la formule genre - degré est une équation reliant le degré d d'une courbe plane irréductible avec son genre arithmétique g par la formule : Ici « courbe plane » signifie que est une courbe fermée dans le plan projectif . Si la courbe est non singulière, le genre géométrique et le genre arithmétique sont égaux, mais si la courbe est singulière, avec seulement des singularités ordinaires, le genre géométrique a priori est plus petit. Plus précisément, une singularité ordinaire de multiplicité r diminue le genre de . (fr)
  • In matematica, e in particolare nella geometria algebrica classica, la formula genere-grado lega il grado di una curva piana che ammette solo singolarità ordinarie con il suo genere geometrico mediante la formula: dove è la molteplicità del punto della curva. Se la curva è non singolare, le molteplicità sono tutte uguali a e si ha la formula in tal caso il e il della curva coincidono. (it)
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