Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 196
... ( D ) > 0 if and only if D divisor . is linearly equivalent to an effective 8-12 . Show that deg ( D ) = 0 and ( D ) > 0 if and only if D = 0 . 8-13 * . Suppose ( D ) > 0 , and let f ‡ 0 , f ɛ L ( D ) . Show that f L ( D - P ) for all but ...
... ( D ) > 0 if and only if D divisor . is linearly equivalent to an effective 8-12 . Show that deg ( D ) = 0 and ( D ) > 0 if and only if D = 0 . 8-13 * . Suppose ( D ) > 0 , and let f ‡ 0 , f ɛ L ( D ) . Show that f L ( D - P ) for all but ...
Page 197
... D = D ' > Do ' { P ε X | > 0 and П ( y - y ( P ) ) Ρετ mp mp Then · whenever ord ( y ) ≥0 . If ordp ( y ) < 0 , so a large r will take care of this . If ( D ) = deg ( D ) + 1 - g , and then ( D ) deg ( D ) + 1 g . = COROLLARY 2. If x ɛ K , ...
... D = D ' > Do ' { P ε X | > 0 and П ( y - y ( P ) ) Ρετ mp mp Then · whenever ord ( y ) ≥0 . If ordp ( y ) < 0 , so a large r will take care of this . If ( D ) = deg ( D ) + 1 - g , and then ( D ) deg ( D ) + 1 g . = COROLLARY 2. If x ɛ K , ...
Page 211
... deg ( D ) + 1 - g + & ( W - D ) . Since g ( W ) ( Cor . to Prop . 8 ) Case 1 : ( W - D ) = 0 . l and ↓ ( W ) ≤ b ( W - D ) + deg ( D ) ( Problem 8-8 ) , we have deg ( D ) g in this case ... ( D ) = & ( D + P RIEMANN - ROCH THEOREM 211.
... deg ( D ) + 1 - g + & ( W - D ) . Since g ( W ) ( Cor . to Prop . 8 ) Case 1 : ( W - D ) = 0 . l and ↓ ( W ) ≤ b ( W - D ) + deg ( D ) ( Problem 8-8 ) , we have deg ( D ) g in this case ... ( D ) = & ( D + P RIEMANN - ROCH THEOREM 211.
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