Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems

C. A. M. Peters

Compositio Mathematica (1990)

  • Volume: 75, Issue: 1, page 113-126
  • ISSN: 0010-437X

How to cite

top

Peters, C. A. M.. "Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems." Compositio Mathematica 75.1 (1990): 113-126. <http://eudml.org/doc/90026>.

@article{Peters1990,
author = {Peters, C. A. M.},
journal = {Compositio Mathematica},
keywords = {rigid family of -dimensional polarized abelian varieties; polarized variation of Hodge structure; non-rigid deformation of period maps; Arakelov theorem; non-trivial deformations of families of curves over punctured curves; -surfaces; Enriques surfaces},
language = {eng},
number = {1},
pages = {113-126},
publisher = {Kluwer Academic Publishers},
title = {Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems},
url = {http://eudml.org/doc/90026},
volume = {75},
year = {1990},
}

TY - JOUR
AU - Peters, C. A. M.
TI - Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 75
IS - 1
SP - 113
EP - 126
LA - eng
KW - rigid family of -dimensional polarized abelian varieties; polarized variation of Hodge structure; non-rigid deformation of period maps; Arakelov theorem; non-trivial deformations of families of curves over punctured curves; -surfaces; Enriques surfaces
UR - http://eudml.org/doc/90026
ER -

References

top
  1. [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)]. Zbl0248.14004MR321933
  2. [C-D] Carlson, J., Donagi, R., Hypersurface variations are maximal I. Inv. Math.89 (1987) 371-374. Zbl0639.14003MR894385
  3. [C-T] Carlson, J., Toledo, D., Integral manifolds, harmonic mappings, and the abelian subspace problem, in: Springer Lect. Notes in Math.1352, 1989. Zbl0662.58012MR981818
  4. [D1] Deligne, P., Travaux de Griffiths. Sem. Bourbaki Exp.1969 /1970 Exp. 376. Zbl0208.48601
  5. [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. Zbl0656.14010MR900821
  6. [F] Faltings, G., Arakelov's Theorem for abelian varieties, Inv. Math.7, 3, 337-348 (1983). Zbl0588.14025MR718934
  7. [F1] Flenner, H., The infinitesimal Torelli problem for zero sets of sections of vector bundles, Math. Zeitschr.193, 307-322. Zbl0613.14010MR856158
  8. [G] Griffiths, P., Periods of integrals on algebraic manifolds IIIPubl. Math. I.H.E.S.38, 125-180 (1970). Zbl0212.53503MR282990
  9. [G, S] Griffiths, P., Schmid, W., Locally homogeneous complex manifolds. Acta Math.123, 253-302 (1969). Zbl0209.25701MR259958
  10. [N] Namba, M., On maximal families of compact complex submanifolds of complex manifolds, Tohoku Math. J.24, 581-609 (1972). Zbl0254.32023MR328129
  11. [P1] Peters, C., A criterion for flatness of Hodge bundles and geometric applications, Math. Ann.268, 1-19 (1984). Zbl0548.14004MR744325
  12. [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. Zbl0621.14025MR908910
  13. [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., Boston1983, 399-463. Zbl0523.14009MR728615
  14. [S] Schmid, W., Variation of Hodge structure: the singularities of the period mapping, Inv. Math.22, 211-319 (1974). Zbl0278.14003MR382272
  15. [Si] Simpson, C., Arakelov's Theorem for Hodge structures, preprint 1985/86. 
  16. [Su] Sunada, T., Holomorphic mappings into a compact quotient of symmetric bounded domain, Nag. Math. J.64, 159-175 (1976). Zbl0352.32030MR419848

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.