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476 ¦
Index

S-equivalent bundles, 221 Calabi-Yau manifold, 21
ddc -Lemma, 132 Carlson, J., 255
ˇ Cartan homotopy formula, 203
Cech cohomology, 30
Cartan, H., 30
Abel-Jacobi map, 160 Cartan-Serre theorem, 39
Abel-Jacobi theorem, 174 Cauchy-Riemann equations, 88
abelian variety, 155 Ceresa, G., 173
a¬ne algebraic variety, 30 Chandrasekharan, K., 211
algebraic cycle, 160, 165 Chern character, 50
algebraic surface, 181 Chern class, 45
almost complex structure, 88 Chern, S. S., 163
altitude, 150 Chern-Weil forms, 58
anti-holomorphic Laplacian, 113 Chow group, 166, 170
Artin group, 255 Clemens, C.H., 173
Artin, M., 226 cocycle condition, 20
Atiyah bundle, 218 conformally equivalent complex structures,
Atiyah, M.F., 25, 128, 217, 232 connection, 52
connection, hermitian, 63
Baum, P., 52 connection, holomorphic, 63
Beauville, A., 241 Corlette, K., 248
Bernstein, J., 84 curvature, 54
Bianchi identity, 59 cycle algebraically equivalent to zero, 172
Birkho¬-Bruhat decomposition, 36
Darboux coordinates, 93
Birkho¬-Grothendieck theorem, 32
Darboux theorem, 93
Bloom, T., 18
degeneration of bundles, 38
blow-up, 9, 135
degree of line bundle, 13
Bott, R., 232
Deligne extension, 240
bundle of jets, 37
Deligne, P., 103, 134, 242
Calabi, E., 251 destabilizing subbundle, 220

264
INDEX 265

developing map, 190 geometric genus of surface, 71
di¬erential graded algebra, 132 geometric situation, 243
divisor, 14, 16 Goldman, W., 228, 231
divisor of meromorphic function, 17 Green™s operator, 130
divisor, principal, 15 Gri¬ths intermediate Jacobian, 168
Dolbeault cohomology, 77 Gri¬ths transversality condition, 205
Dolbeault complex, 73 Gri¬ths, Ph., 134, 168, 242
Dolbeault lemma, 73 Grothendieck group, 65, 81
Dolbeault-Grothendieck theorem, 76 Grothendieck-Grouert theorem, 170
domain of holomorphy, 30 group of Hodge type, 255
Donaldson, S., 248
Hard Lefschetz theorem, 122
Drezet, J.-M., 241
Harder G., 220
elliptic surface, 181 harmonic form, 109
energy functional, 248 harmonic function, 98, 181, 192
Euler characteristic of bundle, 44 Harris, B., 173
Euler characteristic of manifold, 139 Hartog™s theorem, 10
hermitian form, 91
faithful Λ-module, 83
hermitian form on vector space, 62
¬ber product, 11
hermitian metric, 91
¬berwise di¬erential form, 202
hermitian symmetric space, 179
¬‚ag, 186
Herrera, M., 18
¬‚at bundle, 201
Higgs bundle, 245
¬‚at connection, 201
Higgs ¬eld, 245
¬‚at morphism, 170
Hirzebruch signature theorem, 179
formal algebra, 134
Hirzebruch, F., 44, 51, 128
Fujiki, A., 252
Hitchin, N., 245
Fulton, W., 52, 173
Hodge cohomology class, 128
fundamental domain, 149
Hodge conjecture, 128
Hodge decomposition, 105
GAGA principle, 166
Hodge ¬ltration, 206
Gauß, 210
Hodge star operator, 109
Gauß, K.F., 207
Hodge structure (mixed), 242
Gauß-Manin connection, 203
Hodge structure (pure), 126, 241
gauge group, 233
Hodge theorem, 109
Gelfand, I.M., 84
holomorphic Laplacian, 113
Gelfand, S., 84
genus, 14 homologous cocycles, 20
266 INDEX

horizontal section, 53 Levi-Civita connection, 56
hyper-K¨hler manifold, 251
a Lie derivative, 203
line bundle, canonical, 12
Igusa, J., 156 line bundle, tautological, 8
indecomposable bundle, 217 Liouville symplectic form, 93
index of critial point, 189 Lobachevsky plane, 90
integrable connection, 201 local system of abelian groups, 197
intersection number, 22
irreducible subvariety, 16 MacPherson, R., 52
isogeny, 158 meromorphic function, 17
isotropic subspace, 106 meromorphic section, 13
Millson, J., 103, 228, 255
Jacobian, 153 Minkowski reduced matrix, 150
Minkowski theory, 150
K3 surface, 72
Moishezon manifold, 134
K¨hler form, 94
a
monodromy representation, 198
K¨hler manifold, 94
a
Morgan, J., 134, 255
K¨hler potential, 97
a
Mori, S., 21
K¨hler, K., 176
a
Morse function, 189
Kapovich, M., 103, 255
Mostow, G., 103
Karshon, Y., 235
Mumford, D., 221
Klein, F., 176
Klyachko, A., 103 Narasimhan, M., 219, 220, 241
Kodaira, K., 21, 156, 179, 184, 216 Narasimhan-Seshadri theorem, 223

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