 -invariant 15 191 194—195
 -minimal 96 142
 -standard equation 150 153
 -surface 109—110 119
 -invariant see "b-invariant" "(b
Abelian surfaces 40 41 75—94
Abelian variety 20 75—91
Albanese map 77—80 100
Albanese variety 75—76
Algebraic cycles 56-69
Algebraic cycles on a rational surface 67
Algebraic equivalence 20 21—22
Ample divisor see "Divisor"
Anti-holomorphic involution 4 8
Arithmetic genus V 7
b-invariant 15
B-morphism 95
Bertini's involution 129
Birational equivalence 54 65-66 100—105 112—130 136
Birational transformation 49 51 106—107
Birationally trivial 66 114 136
Blowing up 49—50 125—126
Brauer — Severi curve 100 102
Brauer — Severi curve, variety 100 109
Canonical divisor see "Divisor"
Chasles's Theorem 115—116
Chern class 21—22 27—28 32 61 81 179
Colliot — Thelene and Sansuc (conjecture of) 66
Colliot — Thelene's conjecture 136
Comessatti characteristic 15
Conjugate function 1
Conjugate manifold 2
Conjugate scheme 3
Conjugate variety 2
Connected components (bounds for the number) 38—39 41—45
Connected components (bounds for the number) of a rational surface 66 71—73 115 130 135
Contracting an exceptional line 50
Cubic surface 44 132—134
Cup-product 27—31 64 69 180
Divisors of real zeros and poles 57 102
Divisors, ample 19 113 179 182
Divisors, canonical 32 112 113 119 120 172
Divisors, Weil, Cartier 19—22
Elementary transformation 105
Elliptic surface (or fibration) 41 95 97 99 139—173 174—177
Elliptic surface (or fibration), K3 surface 40 42 168—171
Empty real part 45—48 64—65 70 79 109 131 192
Enriques surface 100 197—200
Euler characteristic of  9 33 34
Exceptional line of the first kind 51 52 105
Fibration (real) 95
Fibred surface see "Elliptic surface" "Ruled
Galois cohomology 14—16
Galois-Maximal (or GM-variety) 17—18 66 77 107—108
Geiser involution 128 137
General type (surface of) 42—44
Generic surface 63-65
Harnack — Thom — Krasnov inequality 16
Hermite's theorem 163—164
Hirzeburch surface see "-surface"
Hodge decomposition (Galois action on) 10—12
Hodge index theorem 29—30
Hyperelliptic surface 100 174—177
Intersection form 64-65 68 70 71
Intersection index 27
| Invariants of an involution 15 191 194—195
Irrational ruled surface 98—99 103—105
Irregularity V 7 99
Isomorphic real structures 4—5 109—110 188
J-invariant 144
Jacobian fibration 139—140
K3-surface 40 42 168—171 178—196 199
Kaehler class 29 180 182
Kaehler manifold 18
Kaehler surface 28 29 35 39 178
Kharlamov — Gudkov — Kraknov congruence 34
Krasnov's theorem 25 66 188
Lattice 182
Local parameter 166—168 175
Logarithmic transformation 166—168 175
M-surface ((M-r)-surface) 31
Marked K3 surface 183
Minimal surface 52
Moduli for abelian surfaces 91—94
Moduli for abelian varieties 85—91
Moduli for K3-surfaces 186
Monoidal transformations see "Blowing up"
Neron — Severi group 21 37 59 63 66 106
Neron's classification 142—144
Non-orientable surface 54 70 135
Orientable components 54 71 191 193
Ovals of a curve 42—43
Period map 75
Period matrix 76—80
Period of a K3-surface 183
Picard group 20 58—59 63 66-69 82 113 118—119 134
Picard variety 76—77
Polarized Abelian variety 84
Principal polarization 84
Quadric surface 48 131—132 193 196
Quartic surface 40 42 63-64
Quintic surface 40 62-63
Rational ruled surface 97 114—124 125 127
Rational surface 65—74 97 109—138
Real algebraic variety 8
Real basis 78
Real equivalence see "Isomorphic real structures"
Real fib ration 95
Real irreducible divisor 110
Real model 4
Real part 5 8
Real polarization 81
Real sheaf 6
Real structure 3 8
Real Torelli for K3-surfaces 181
Relatively minimal surface 52
Rokhlin's congruence 32—33
Ruled surface 95—108 see
Semi-local basis 78
Smith sequence 13—14 47 72
Special K3-surface 193
Surface of general type see "General type"
Surface over  8—9
Torelli theorem for K3-surfaces 180—181
Twist 20—21
Twisted action 20—21 28
Weierstrass equation 144
Weil divisor see "Divisor"
Weil's theorem 4—5
Wu class 32 61
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