Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Résultats 1-3 sur 13
Page 47
... uniformizing parameter for R ; any other uniformizing parameter is of the form ut , u a unit in R. Let K be the quotient field of R. Then ( when t is fixed ) any non - zero element Ζε κ has a unique expression z = ut ut " , u a unit in ...
... uniformizing parameter for R ; any other uniformizing parameter is of the form ut , u a unit in R. Let K be the quotient field of R. Then ( when t is fixed ) any non - zero element Ζε κ has a unique expression z = ut ut " , u a unit in ...
Page 49
... uniformizing parameter for R , and 2 n≥ 0 there are unique Z ε R such that n λ εκ n λ12t + λt2 + ... + λ t2 + z_t a tn + 1 . ( Hint : n n For z = λ O 1 n uniqueness use Problem 2-29 ; for existence use ( a ) and induction . ) 2-31 ...
... uniformizing parameter for R , and 2 n≥ 0 there are unique Z ε R such that n λ εκ n λ12t + λt2 + ... + λ t2 + z_t a tn + 1 . ( Hint : n n For z = λ O 1 n uniqueness use Problem 2-29 ; for existence use ( a ) and induction . ) 2-31 ...
Page 208
... uniformizing parameter in 2 Op , ( X ) , and dy = = -y2a ( y ̄1 ) , P i ɛ zn . c . i SO ord ( dy ) = -2 . Since F ( P ; ) 0 ( Problem 5-16 ) , both sides of ( 8 ) have order X i -2 at Q • Suppose Q is a place centered at P = ( a , b , 1 ) ...
... uniformizing parameter in 2 Op , ( X ) , and dy = = -y2a ( y ̄1 ) , P i ɛ zn . c . i SO ord ( dy ) = -2 . Since F ( P ; ) 0 ( Problem 5-16 ) , both sides of ( 8 ) have order X i -2 at Q • Suppose Q is a place centered at P = ( a , b , 1 ) ...
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 | |
26 autres sections non affichées
Autres éditions - Tout afficher
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