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On the Classification of Rational Plane Curves of Type (d,m): Rational Plane Curves of Types (d,d-2) and (d,d-3,1) - Couverture souple

Abuelhassan, Mohammed

 
9783844399882: On the Classification of Rational Plane Curves of Type (d,m): Rational Plane Curves of Types (d,d-2) and (d,d-3,1)
Couverture souple
ISBN 10 : 3844399887 ISBN 13 : 9783844399882
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

Let C⊂P²=P²(C) be a rational plane curve of degree d and let ν denote the maximal multiplicity of the singular points of C. We say that C is of type (d,ν). Let P∈C be a singular point, and let r_{P} be the number of the branches of C at P. Set ι(C)=∑_{P∈Sing(C)}(r_{P}-1). We say that C is of type (d,ν,ι) if C is of type (d,ν) and ι=ι(C). We classify all rational plane curves of type (d,d-2). We give the complete list of all rational plane curves of type (d,d-2). In particular, we provide an inductive algorithm to construct such curves. Furthermore, we show that any such curve C is transformable into a line by a Cremona transformation. We also construct some classes of rational plane curves of type (d,d-3,1).

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Let C⊂P²=P²(C) be a rational plane curve of degree d and let ν denote the maximal multiplicity of the singular points of C. We say that C is of type (d,ν). Let P∈C be a singular point, and let r_{P} be the number of the branches of C at P. Set ι(C)=∑_{P∈Sing(C)}(r_{P}-1). We say that C is of type (d,ν,ι) if C is of type (d,ν) and ι=ι(C). We classify all rational plane curves of type (d,d-2). We give the complete list of all rational plane curves of type (d,d-2). In particular, we provide an inductive algorithm to construct such curves. Furthermore, we show that any such curve C is transformable into a line by a Cremona transformation. We also construct some classes of rational plane curves of type (d,d-3,1).

Biographie de l'auteur

A lecturer in Algebraic Geometry, Mathematics department, Faculty of science, Sohag University, Egypt.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3844399887
ISBN 13 
9783844399882
Reliure
Broché
Nombre de pages
100
Coordonnées du fabricant
non disponible
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