Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 66
... tangent line to is called a double point , if m = 3 , a triple point , Since F is a form in two variables , we can write r i m where the L are distinct lines ( Chapter 2 , = [ ] ; Prop . 5 , Cor . ) . The L are called the tangent lines ...
... tangent line to is called a double point , if m = 3 , a triple point , Since F is a form in two variables , we can write r i m where the L are distinct lines ( Chapter 2 , = [ ] ; Prop . 5 , Cor . ) . The L are called the tangent lines ...
Page 67
... tangent lines to F at P , is the multiplicity of the tangent , etc. Note that T takes the points of T tangents to F ... line to a simple point coincide . P = ( 0,0 ) Problems . 3-1 . Prove that in the above example is the only multiple point ...
... tangent lines to F at P , is the multiplicity of the tangent , etc. Note that T takes the points of T tangents to F ... line to a simple point coincide . P = ( 0,0 ) Problems . 3-1 . Prove that in the above example is the only multiple point ...
Page 75
... tangent line to F at P is different from the tangent line to Gat P. We want the intersection number to be one exactly when F and meet transversally at P. More generally , we require ( 5 ) I ( P , FN G ) ≥ mp ( F ) mp ( G ) , with ...
... tangent line to F at P is different from the tangent line to Gat P. We want the intersection number to be one exactly when F and meet transversally at P. More generally , we require ( 5 ) I ( P , FN G ) ≥ mp ( F ) mp ( G ) , with ...
Table des matières
Chapter One Affine Algebraic Sets | 1 |
Chapter Two Affine Varieties | 38 |
35 | 51 |
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 denote div(G div(z divisor element F and G F ɛ finite number flex follows form of degree function field Hint hyperplane hypersurface induced integer intersection number isomorphism LEMMA Let F linear local ring maximal ideal module-finite morphism mp(F Noether's non-singular non-zero Nullstellensatz Op(C Op(F 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 resp ring homomorphism simple point subring subvariety Suppose tangent line uniformizing parameter unique vector space zero ε Ι Ρε