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Kodaira-Spencer map, 215 Neron-Severi group, 173
Kostant, B., 163 Newlander, A., 89
Koszul complex, 41 Nierenberg, L., 89
Kronheimer, P., 252 Nijenhuis tensor, 89
Kummer surface, 140 Novikov conjecture, 149
Kummer, E., 176
Oka, K., 30
Lagrangian subspace, 106 order of function along subvariety, 16
Laplace operator, 108 orientation class, 51
Laplacian, 108
Lefschetz (1,1) theorem, 128 parabolic cohomology, 238
Lefschetz operator, 111 paved varieties, 184
Lefschetz theorem, 188 Piatetski-Shapiro theorem, 178
Legendre family, 206 Picard group, 13, 15
INDEX 267

pluriharmonic function, 192 Siegel space, 144
plurisubharmonic function, 192 Siegel-reduced matrix, 152
Poincar´, H., 158
e signature, 137
polarization of torus, 157 simple vector bundle, 219
polystable Higgs bundle, 249 Simpson, C., 245, 250, 253
potential of connection, 53 Siu, Y.-T., 255
Pressley, A., 36 Spencer, D.C., 216
primitive cohomology, 123 Splitting principle, 49
principal polarization, 157 stable bundle, 220
principally polarized abelian variety, 157
stable Higgs bundle, 249
projective quadric, 185 Stein manifold, 30
projective space, 6 subharmonic function, 192
pull-back, 10 Sullivan, D., 134, 255
pull-back of connection, 60 Suslin, A., 81
symplectic form, 93
quasi-isomorphic algebras, 133 symplectic structue, 93
Quillen, D., 81
theta divisor. generalized, 241
Ramanan, S., 221
theta function, 27
reduction of structure group, 246
theta function, generalized, 241
regular surface, 181
Todd class, 51
Riemann surface, 89
Toledo, D., 255
Riemann-Roch-Hirzebruch theorem, 52
Torelli map, 149
Riemann-Siegel theorem, 144
Torelli theorem, 149
tube domain, 179
Sampson, J., 255
twistor space, 251
scalar endomorphism, 219
section of bundle, 5
unimodular tuple, 150
section of sheaf, 200
universal bundle, 240
Segal, G., 36
universality property, 11
semistable bundle, 220
Serre conjecture, 81 variation of Hodge structure, 242
Serre duality theorem, 43 vector bundle, holomorphic, 6
Serre vanishing theorem, 45 vector bundle, real, 4
Serre, J-P., 15, 39, 45, 166 Verlinde formula, 241
Seshadri, C., 219
Weierstraß cubic curve, 106
sheaf of abelian groups, 199
Shiota, M., 149 Weil, A., 156, 163, 184
268 INDEX

Whitney sum formula, 47
Witt, E., 177

Yau, S. T., 142, 251

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