Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems
Peters, C. A. M.
Compositio Mathematica, Tome 76 (1990), p. 113-126 / Harvested from Numdam
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Publié le : 1990-01-01
@article{CM_1990__75_1_113_0,
     author = {Peters, C. A. M.},
     title = {Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems},
     journal = {Compositio Mathematica},
     volume = {76},
     year = {1990},
     pages = {113-126},
     mrnumber = {1059957},
     zbl = {0743.14006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1990__75_1_113_0}
}

Peters, C. A. M. Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems. Compositio Mathematica, Tome 76 (1990) pp. 113-126. http://gdmltest.u-ga.fr/item/CM_1990__75_1_113_0/

[A] Arakelov, A., Families of algebraic curves with fixed degeneracies, Izv. Ak. Nauk. S.S.SR., ser. Math. 35 (1971) [Math. U.S.S.R. Izv. 5, 1277-1302 (1971)]. | MR 321933 | Zbl 0248.14004

[C-D] Carlson, J., Donagi, R., Hypersurface variations are maximal I. Inv. Math. 89 (1987) 371-374. | MR 894385 | Zbl 0639.14003

[C-T] Carlson, J., Toledo, D., Integral manifolds, harmonic mappings, and the abelian subspace problem, in: Springer Lect. Notes in Math. 1352, 1989. | MR 981818 | Zbl 0662.58012

[D1] Deligne, P., Travaux de Griffiths. Sem. Bourbaki Exp. 1969 /1970 Exp. 376. | Numdam | Zbl 0208.48601

[D2] Deligne, P., Un théorème de finitude pour la monodromie, in "Discrete groups in geometry and analysis" Progr. in Math. 67, Birkh. 1987, p. 1-19. | MR 900821 | Zbl 0656.14010

[F] Faltings, G., Arakelov's Theorem for abelian varieties, Inv. Math. 7, 3, 337-348 (1983). | MR 718934 | Zbl 0588.14025

[F1] Flenner, H., The infinitesimal Torelli problem for zero sets of sections of vector bundles, Math. Zeitschr. 193, 307-322. | MR 856158 | Zbl 0613.14010

[G] Griffiths, P., Periods of integrals on algebraic manifolds III Publ. Math. I.H.E.S. 38, 125-180 (1970). | Numdam | MR 282990 | Zbl 0212.53503

[G, S] Griffiths, P., Schmid, W., Locally homogeneous complex manifolds. Acta Math. 123, 253-302 (1969). | MR 259958 | Zbl 0209.25701

[N] Namba, M., On maximal families of compact complex submanifolds of complex manifolds, Tohoku Math. J. 24, 581-609 (1972). | MR 328129 | Zbl 0254.32023

[P1] Peters, C., A criterion for flatness of Hodge bundles and geometric applications, Math. Ann. 268, 1-19 (1984). | MR 744325 | Zbl 0548.14004

[P2] Peters, C., On Arakelov's finiteness theorem for higher dimensional manifolds, Rend. Sem. Mat. Univ. e Polit. Torino, Convegno su Algebraic Varieties of small codimension, 43-50, 1986. | MR 908910 | Zbl 0621.14025

[P-S] Peters, C., Steenbrink, J., Infinitesimal variations of Hodge structure and the generic Torelli problem for projective hypersurfaces. Progress in Math. # 30 Birkh. Verl., Boston 1983, 399-463. | MR 728615 | Zbl 0523.14009

[S] Schmid, W., Variation of Hodge structure: the singularities of the period mapping, Inv. Math. 22, 211-319 (1974). | MR 382272 | Zbl 0278.14003

[Si] Simpson, C., Arakelov's Theorem for Hodge structures, preprint 1985/86.

[Su] Sunada, T., Holomorphic mappings into a compact quotient of symmetric bounded domain, Nag. Math. J. 64, 159-175 (1976). | MR 419848 | Zbl 0352.32030