Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 24
... irreducible curve for any algebraically closed field k , and any λεκ . 0 1-36 . Let ( x2 - x2 , y2 + x2 ) ≤ ¢ [ X , Y ] . I = dim ( C [ X , Y ] / I ) . C 1-37 * . Find V ( I ) and Let K be any field , F ε K [ X ] a polynomial of degree ...
... irreducible curve for any algebraically closed field k , and any λεκ . 0 1-36 . Let ( x2 - x2 , y2 + x2 ) ≤ ¢ [ X , Y ] . I = dim ( C [ X , Y ] / I ) . C 1-37 * . Find V ( I ) and Let K be any field , F ε K [ X ] a polynomial of degree ...
Page 106
... irreducible curve . ( a ) Show that Fx , Fy , or F , 0 . Z ( b ) Show that F has only a finite number of multiple points . 5-9 . ( a ) Let F be an irreducible conic , P = ( 0,1,0 ) a simple point on F , and 2 = 0 F at P. Show that F ...
... irreducible curve . ( a ) Show that Fx , Fy , or F , 0 . Z ( b ) Show that F has only a finite number of multiple points . 5-9 . ( a ) Let F be an irreducible conic , P = ( 0,1,0 ) a simple point on F , and 2 = 0 F at P. Show that F ...
Page 118
... irreducible conics are non - singular , and an irreducible cubic can have at most one double point . Letting n = 4 we see that an irreducible quartic has at most three double points or one triple point , -1 y2 Z etc. Note that the curve ...
... irreducible conics are non - singular , and an irreducible cubic can have at most one double point . Letting n = 4 we see that an irreducible quartic has at most three double points or one triple point , -1 y2 Z etc. Note that the curve ...
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