Compact Kähler manifolds with compactifiable universal cover

Benoît Claudon; Andreas Höring

Bulletin de la Société Mathématique de France (2013)

  • Volume: 141, Issue: 2, page 355-375
  • ISSN: 0037-9484

Abstract

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In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.

How to cite

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Claudon, Benoît, and Höring, Andreas. "Compact Kähler manifolds with compactifiable universal cover." Bulletin de la Société Mathématique de France 141.2 (2013): 355-375. <http://eudml.org/doc/272722>.

@article{Claudon2013,
abstract = {In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.},
author = {Claudon, Benoît, Höring, Andreas},
journal = {Bulletin de la Société Mathématique de France},
keywords = {universal cover; Iitaka’s conjecture},
language = {eng},
number = {2},
pages = {355-375},
publisher = {Société mathématique de France},
title = {Compact Kähler manifolds with compactifiable universal cover},
url = {http://eudml.org/doc/272722},
volume = {141},
year = {2013},
}

TY - JOUR
AU - Claudon, Benoît
AU - Höring, Andreas
TI - Compact Kähler manifolds with compactifiable universal cover
JO - Bulletin de la Société Mathématique de France
PY - 2013
PB - Société mathématique de France
VL - 141
IS - 2
SP - 355
EP - 375
AB - In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.
LA - eng
KW - universal cover; Iitaka’s conjecture
UR - http://eudml.org/doc/272722
ER -

References

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  1. [1] D. Barlet – « Espace analytique réduit des cycles analytiques complexes compacts d’un espace analytique complexe de dimension finie », in Fonctions de plusieurs variables complexes, II (Sém. François Norguet, 1974–1975), Springer, 1975, p. 1–158. Lecture Notes in Math., Vol. 482. MR399503
  2. [2] S. Boucksom, J.-P. Demailly, M. Păun & T. Peternell – « The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension », to appear in Journal of Alg. Geometry. Zbl1267.32017
  3. [3] F. Campana – « Algébricité et compacité dans l’espace des cycles d’un espace analytique complexe », Math. Ann.251 (1980), p. 7–18. Zbl0445.32021MR583821
  4. [4] —, « Coréduction algébrique d’un espace analytique faiblement kählérien compact », Invent. Math.63 (1981), p. 187–223. Zbl0436.32024MR610537
  5. [5] —, « Réduction d’Albanese d’un morphisme propre et faiblement kählérien. II. Groupes d’automorphismes relatifs », Compositio Math.54 (1985), p. 399–416. Zbl0609.32008MR791508
  6. [6] —, « Rigidité des fibres des réductions algébriques », J. reine angew. Math. 385 (1988), p. 152–160. Zbl0636.32015MR931218
  7. [7] —, « Remarques sur le revêtement universel des variétés kählériennes compactes », Bull. Soc. Math. France122 (1994), p. 255–284. MR1273904
  8. [8] —, « Connexité abélienne des variétés kählériennes compactes », Bull. Soc. Math. France126 (1998), p. 483–506. MR1693441
  9. [9] —, « Orbifolds, special varieties and classification theory », Ann. Inst. Fourier (Grenoble) 54 (2004), p. 499–630. Zbl1062.14014MR2097416
  10. [10] F. Campana & B. Claudon – « Abelianity conjecture for special compact Kähler threefolds », preprint arXiv:1107.0168, to appear in PEMS, special volume in honour of V. Shokurov. 
  11. [11] F. Campana & M. Păun – « Une généralisation du théorème de Kobayashi-Ochiai », Manuscripta Math.125 (2008), p. 411–426. MR2392879
  12. [12] F. Campana & T. Peternell – « Complex threefolds with non-trivial holomorphic 2 -forms », J. Algebraic Geom.9 (2000), p. 223–264. Zbl0994.32016MR1735771
  13. [13] F. Campana & Q. Zhang – « Compact Kähler threefolds of π 1 -general type », in Recent progress in arithmetic and algebraic geometry, Contemp. Math., vol. 386, Amer. Math. Soc., 2005, p. 1–12. MR2182767
  14. [14] B. Claudon, A. Höring & J. Kollár – « Algebraic varieties with quasi-projective universal cover », to appear in J. reine angew. Math. Zbl1278.14030
  15. [15] O. Debarre – Higher-dimensional algebraic geometry, Universitext, Springer, 2001. MR1841091
  16. [16] J. Fernandez de Bobadilla & J. Kollár – « Homotopically trivial deformations », preprint arXiv:1201.2904. MR2928935
  17. [17] G. Fischer & O. Forster – « Ein Endlichkeitssatz für Hyperflächen auf kompakten komplexen Räumen », J. reine angew. Math. 306 (1979), p. 88–93. MR524649
  18. [18] A. Fujiki – « On automorphism groups of compact Kähler manifolds », Invent. Math.44 (1978), p. 225–258. Zbl0367.32004MR481142
  19. [19] —, « On the structure of compact complex manifolds in 𝒞 », in Algebraic varieties and analytic varieties (Tokyo, 1981), Adv. Stud. Pure Math., vol. 1, North-Holland, 1983, p. 231–302. MR715653
  20. [20] A. Höring, T. Peternell & I. Radloff – « Uniformisation in dimension four: towards a conjecture of Iitaka », to appear in Math. Zeitschrift. 
  21. [21] P. Ionescu – « Generalized adjunction and applications », Math. Proc. Cambridge Philos. Soc.99 (1986), p. 457–472. MR830359
  22. [22] Y. Kawamata – « Characterization of abelian varieties », Compositio Math.43 (1981), p. 253–276. Zbl0471.14022MR622451
  23. [23] S. Kobayashi & T. Ochiai – « Meromorphic mappings onto compact complex spaces of general type », Invent. Math.31 (1975), p. 7–16. Zbl0331.32020MR402127
  24. [24] J. Kollár – « Shafarevich maps and plurigenera of algebraic varieties », Invent. Math.113 (1993), p. 177–215. Zbl0819.14006MR1223229
  25. [25] J. Kollár & J. Pardon – « Algebraic varieties with semialgebraic universal cover », J. Topol.5 (2012), p. 199–212. Zbl1243.14008MR2897053
  26. [26] D. I. Lieberman – « Compactness of the Chow scheme: applications to automorphisms and deformations of Kähler manifolds », in Fonctions de plusieurs variables complexes, III (Sém. François Norguet, 1975–1977), Lecture Notes in Math., vol. 670, Springer, 1978, p. 140–186. MR521918
  27. [27] Y. Miyaoka & S. Mori – « A numerical criterion for uniruledness », Ann. of Math.124 (1986), p. 65–69. MR847952
  28. [28] P. Molino – Riemannian foliations, Progress in Math., vol. 73, Birkhäuser, 1988. MR932463
  29. [29] N. Nakayama – « Compact Kähler manifolds whose universal covering spaces are biholomorphic to 𝐂 n », RIMS preprint, 1999. 
  30. [30] —, « Projective algebraic varieties whose universal covering spaces are biholomorphic to 𝐂 n », J. Math. Soc. Japan51 (1999), p. 643–654. Zbl0948.14009MR1691481
  31. [31] M. Reid – « Tendencious survey of 3 -folds », in Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., 1987, p. 333–344. MR927962
  32. [32] J. A. Wiśniewski – « On contractions of extremal rays of Fano manifolds », J. reine angew. Math. 417 (1991), p. 141–157. Zbl0721.14023MR1103910

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