Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 68
... curve in part ( a ) that is contained in A2 ( R ) 2 3-3 . If a curve F of degree n has a point P of multiplicity n , show that F consists of n lines through P ( not necessarily distinct ) . 3-4 . Let Р be a double point on a curve F ...
... curve in part ( a ) that is contained in A2 ( R ) 2 3-3 . If a curve F of degree n has a point P of multiplicity n , show that F consists of n lines through P ( not necessarily distinct ) . 3-4 . Let Р be a double point on a curve F ...
Page 71
... ( F ) , we write ord ( G ) If P is a simple we write ord g is the image of G in instead of ord ( g ) . F point on a reducible curve F , F i where F. is the i instead of ord , component of F containing P. Suppose P is a simple point on F ...
... ( F ) , we write ord ( G ) If P is a simple we write ord g is the image of G in instead of ord ( g ) . F point on a reducible curve F , F i where F. is the i instead of ord , component of F containing P. Suppose P is a simple point on F ...
Page 178
... F ( PS ) , T ̄1 ( s ) ʼn v ( XYZ ) Τ = Ø . Then there is a neighborhood of S on F which is isormorphic to an open set on ( FT ) ' . ( b ) If S is a finite set of simple points on a with only ordinary plane curve F , there is a curve F ...
... F ( PS ) , T ̄1 ( s ) ʼn v ( XYZ ) Τ = Ø . Then there is a neighborhood of S on F which is isormorphic to an open set on ( FT ) ' . ( b ) If S is a finite set of simple points on a with only ordinary plane curve F , there is a curve F ...
Table des matières
Chapter One Affine Algebraic Sets 1 Algebraic Preliminaries | 1 |
Affine Space and Algebraic Sets | 7 |
The Ideal of a Set of Points | 10 |
Droits d'auteur | |
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Expressions et termes fréquents
affine variety algebraic set algebraic subset algebraically closed assume Bezout's Theorem birational birationally equivalent called change of coordinates Chapter closed subvariety comaximal COROLLARY curve F curve of degree defined deg(D deg(F denote div(G div(z divisor element F and G f ɛ finite number follows form of degree function field Hint homogeneous hyperplane hypersurface induced integer intersection number isomorphism k[X₁ LEMMA Let F linear local ring maximal ideal module-finite morphism mp(F Noether's non-singular non-zero Nullstellensatz Op(C Op(V open subvariety ordinary multiple points plane curve point on F polynomial map Problem projective change projective curve projective plane curve projective variety Proof Prop PROPOSITION quadratic transformation quotient field R-module rational function residue ring homomorphism simple point subring subvariety Suppose tangent line uniformizing parameter unique V₁ vector space Xn+1 zero Ρε