Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 190
... div ( F ) = = ( 6-1 ) f ( Q ) QEX multiple points . For each σε Χ , let Define the divisor E = Σ ( r - 1 ) Q . E QεX rq = m ₤ ( Q ) ( c ) . is an effective divisor of degree Er ( -1 ) . Any plane curve that div ( G ) E is called an ...
... div ( F ) = = ( 6-1 ) f ( Q ) QEX multiple points . For each σε Χ , let Define the divisor E = Σ ( r - 1 ) Q . E QεX rq = m ₤ ( Q ) ( c ) . is an effective divisor of degree Er ( -1 ) . Any plane curve that div ( G ) E is called an ...
Page 207
... g = a ε Op ( X ) by Prop . 7 , and likewise dt so ord ( f ) = ord ( 8 ) . g / f ε Op ( x ) , If 0 7 wε N , the divisor of w , div ( w ) , is defined to be Σ ord ( w ) P . In Prop . 8 we shall show PEX # that only finitely many ordp ( w ) ...
... g = a ε Op ( X ) by Prop . 7 , and likewise dt so ord ( f ) = ord ( 8 ) . g / f ε Op ( x ) , If 0 7 wε N , the divisor of w , div ( w ) , is defined to be Σ ord ( w ) P . In Prop . 8 we shall show PEX # that only finitely many ordp ( w ) ...
Page 223
... G ( f ) 146 37,137 tr . deg K 149 FT , IT , 40 dim ( X ) 150 k ( V ) 42,92 g * ( C ) 176 P Op ( v ) 43,93,135 deg ( D ) 187 f ( P ) M2 ( V ) 43,93,135 div ( G ) , div ( z ) 188 44,93 ( 2 ) 09 ( 2 ) ∞ 188 DVR , ord 47 DE D ' 189 k [ [ X ] ...
... G ( f ) 146 37,137 tr . deg K 149 FT , IT , 40 dim ( X ) 150 k ( V ) 42,92 g * ( C ) 176 P Op ( v ) 43,93,135 deg ( D ) 187 f ( P ) M2 ( V ) 43,93,135 div ( G ) , div ( z ) 188 44,93 ( 2 ) 09 ( 2 ) ∞ 188 DVR , ord 47 DE D ' 189 k [ [ X ] ...
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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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