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Reid M. Ч Undergraduate algebraic geometry
Reid M. Ч Undergraduate algebraic geometry

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Ќазвание: Undergraduate algebraic geometry

јвтор: Reid M.

јннотаци€:

Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory.


язык: en

–убрика: ћатематика/јлгебра/јлгебраическа€ геометри€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1988

 оличество страниц: 131

ƒобавлена в каталог: 12.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
a.c.c. (ascending chain condition)      48Ч49 53 55 63
Abstract variety      4 79Ч80 117Ч118
Affine change of coordinates      12 24
Affine coordinates      14 38 43 111
Affine covering of projective variety      83
Affine curve      39 45 79
Affine piece of projective variety      13 38 79 83Ч84 92
Affine space $\mathbb{A}^n_k$      50 53 60 64 66 69 77 79 89 94 100 113 121
Affine variety      4 48 50 70 74 78
Aftine cone over projective variety      81 82
Aftine scheme      118
Algebraic (sub-) set      50Ч55 64 66 72 78 81Ч86
Algebraically closed field      52 54 55 64 71 77 115Ч116 118 119 120
Algebraically independent      59 89 97 100
Asymptotic line      9 12 14 60 111
BezoutТs Theorem      17Ч18 33 35Ч36
Birational equivalence      87Ч89 99 100Ч101 107
Birational maps      87Ч89 91 92 99 100Ч101
Blow-up      100Ч101
Categories of geometry      2Ч4 46
Category theory      4 114 118 121
Characteristic p      4 14 16 24 28 61Ч62 123
Classification of varieties      43Ч47 115
Complete variety      117
Complex analytic geometry      3 36 43Ч47 95 116
Complex function theory      6 45Ч47 112 116
conic      9Ч20 25Ч33 37Ч38 45 85 93
Coordinate ring k[V]      66Ч72 73 74 75 118 121
Cubic curve      1 2 7 27Ч42 43Ч44 75Ч77 79 92 115
Cubic surface      102Ч111 114 115
Cuspidal cubic      27 41 68 74 103 111
Denominator of a rational function      4 68 72 76Ч77 78
Dense open set      36 51 67 71 72 73 88 95 97 99
DIMENSION      2 57 59 60 62 64 97 99 102 123Ч124
Diophantine problems      1 9Ч10 24 28 41Ч42 45Ч47 123
Discrete valuation ring (d.v.r.)      122 123
Discriminant      22 23 106
Domain of definition dom f      71Ч73 77 78 83Ч84 85 87 91
Dominant      73Ч74 87
Elimination theory      25 57 64 104Ч105
Empty set $\emptyset$      45 52 53 55 73 82
Equivalence of categories $V \mapsto k[V]$      69 118 120
Finite algebra      4 57Ч58 59 60 61 64
Finitely generated algebra      4 49 54 57Ч59 71 118 122
Finitely generated ideal      48 49 50 81
FORM      16Ч17 22 25 30 99
Function field k(V)      62Ч63 71 73 74 78 83 85 87 88 89 97 99 112 121 122
Generic point      119 120Ч121 122
Genus of a curve      43Ч47 115
Group law on cubic      33Ч36 39Ч41 46 76
Homogeneous ideal      80Ч81 84
Homogeneous polynomial (= form)      16Ч17 22 25 30 80Ч81 99Ч100
Homogeneous V-I correspondences      81Ч82
Hypersurface      50 56Ч57 62Ч63 64 88Ч89 94Ч95 99 101
Inflexion      34 38 41 103 111
Infniite descent      29 42
Intersection of plane curves      17 33 35Ч36 64
Intersection of two conies      20Ч25 115
Intersection of two quadrics      91Ч92 115
Irreducible algebraic set      33 52Ч53 55 57 63 67 71 78 82 84 92 95
Irreducible hypersurface      56Ч57 64
Isomorphism      4 68 70 74Ч75 77 78 79 85 87 90 92 93 99
Jacobson ring      118
Jokes (not for exam)      51 55 69 91 114
Linear projection      10 60 65 68 86 92 107
Linear system of plane curves      18Ч20 30Ч33
Local ring $\mathcal{O}_{V,P}$      71 83 116 122
Localisation $A[S^{-1}]$      49 63 122
Maximal ideal $m_P$      54 55 64 118 119 120
Military funding      13 112 113
Moduli      46 47 114 121 123
Morphism (= regular map)      4 36 74 76 77 80 85 90 93 107 111
Multiple roots, multiplicities      16Ч17 34 35 38 40 52 94 102 106
Nodal cubic      27 40 68 78
Noether normalisation      59Ч62 64
Noetherian property of Zariski topology      53
Noetherian ring      48Ч49 63
Non-singular      2 33 92 94Ч95 97 99 101 102 107 111 116 122
Non-singular cubic      see УCubic curveФ
Normal form of cubic      38 41
Nullstellensatz      30 54 72 81Ч82 118
Number theory      see УDiophantine problemsФ
Open set      see УDense open setФ or УStandard open setФ
Ouasiprojective variety      4 117
Parallelism      11 12 14 15 25 60
Parametrised curve      9Ч10 15 17Ч18 24 27Ч28 31 40 45 47 68 74 77Ч78 85 86 88 121
Pascal mystic hexagon      36Ч37
Pencil of conies      20 21Ч25
Point at infinity      9 12 13 14 16 17 38 39 40 43 60 76 111
Polynomial curve      27 57 64
Polynomial function      2 3 4 51 66Ч70 72 96
Polynomial map      2 67Ч70 74 77 78
Prime ideal      52 54Ч55 60 61 118 120
Prime spectrum Spec A      118 119 122
Primitive Element Theorem      62
Principal ideal domain (PID)      63
Product of varieties      78 89 92
Projective algebraic geometry      117Ч118
Projective change of coordinates      11Ч12 41
Projective curve      13 24 44 75
Projective equivalence      15 18
Projective geometry      9 11 79
Projective line $\mathbb{P}^1$      16 43 79 80 85 90
Projective plane $\mathbb{P}^2$      9 11Ч20 17 25 30Ч33 38 47 79 86 107
Projective space $\mathbb{P}^3$, $\mathbb{P}^n$      4 6 60 80 81 85 86 89 91 100 102 108
Projective variety      4 13 79Ч90 117
Projective variety and non-singularity      99Ч100
Quadric surface      64 86 90 91 108 109 110
Radical rad $I = \sqrt{I}$      54Ч55 63 81Ч82
Rational curve      45 85 91 115 118
Rational function      2 3 4 28 45 68 71Ч72 76 78 82Ч83 116
Rational map      4 28 72Ч74 76Ч78 84Ч87 91 107 111 121
Rational normal curve      85 91
Rational variety      45 88 107 115 117 118 123
Real geometry      6Ч7 115
Regular function      2 4 71Ч72 77 78 116 122
Regular function on a projective variety      80 82 83 90 92 116
Regular map (= morphism)      2 4 6 71Ч72 74 77 78 85 90 92 111
Resultant      25 64 104Ч105
Riemann sphere      43
Riemann surface      43 45 112
Roots of a form in two variables      see УZeroФ
Segre embedding      89
Separability      61Ч62 95 123
singular      2 94 95 97 100 101 102 111
Singular conic      21Ч22 25 107
Singular cubic      see УNodalФ or УCuspidal cubicФ
Singular cubic surface      111
Singularity      7 28 94 100Ч101 116
Singularity theory      2 6 100Ч101 115
Standard affine pieces $V_{(i)}$      13 38 79 83Ч84 92
Standard open set Vf      55 72 74Ч75 98
Tangent space $T_PV$      2 33 34 40 41 94Ч100 103 111 123
topology      see УZariski topologyФ
Topology of a curve      43Ч44 46
Transcendence degree tr $deg_kK$      63 88 89 97 100
Transversal of lines      108
Twisted cubic      85 91 114
Unique factorisation domain (UFD)      28 54 63 71 78
V-I correspondence      50Ч51 52 53 54 55 60 63Ч64 66Ч67 81Ч82 84
Variety      50 57 70 80 88 89 97 99 102 113 116 117Ч122
Veronese surface      93
Zariski topology      36 50Ч51 64 67 71 73 75 78 81 83 84 89 92 95 116 118 119 120
Zero of a form      16Ч17 22 23 25 31 34 38 41 104 106
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