Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 32
... Suppose L ' F ( y ) = 0 . such that F ( y ) to in L , then F ( x ) = 0 . = 0 . is a field extension of K , y ɛ L ' Show that the homomorphism from K [ X ] L ' which takes X to y induces an isomorphism of L with K ( y ) . ( c ) With L ...
... Suppose L ' F ( y ) = 0 . such that F ( y ) to in L , then F ( x ) = 0 . = 0 . is a field extension of K , y ɛ L ' Show that the homomorphism from K [ X ] L ' which takes X to y induces an isomorphism of L with K ( y ) . ( c ) With L ...
Page 48
... Suppose RCS K , SCK , and S is also a DVR . Suppose the maximal ideal of S S = R. contains M. Show that 2-27 . Show that the DVR's of Problem 2-24 are the only DVR's with quotient field k ( X ) which contain k . Show that those of 2-25 ...
... Suppose RCS K , SCK , and S is also a DVR . Suppose the maximal ideal of S S = R. contains M. Show that 2-27 . Show that the DVR's of Problem 2-24 are the only DVR's with quotient field k ( X ) which contain k . Show that those of 2-25 ...
Page 82
... Suppose L = { a + tb , c + ta ) | t ɛ k } . Factor G ( T ) = ɛ I ( T - λ ) , e Let L be a line Define G ( T ) = = F ... Suppose P is a double point on a curve F , and has only one tangent L at P. suppose F ( a ) Show that I ( P , FL ) ...
... Suppose L = { a + tb , c + ta ) | t ɛ k } . Factor G ( T ) = ɛ I ( T - λ ) , e Let L be a line Define G ( T ) = = F ... Suppose P is a double point on a curve F , and has only one tangent L at P. suppose F ( a ) Show that I ( P , FL ) ...
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