Towards a Mori theory on compact Kähler threefolds III

Thomas Peternell

Bulletin de la Société Mathématique de France (2001)

  • Volume: 129, Issue: 3, page 339-356
  • ISSN: 0037-9484

Abstract

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Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e. K X is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of K X is generated by global sections); unless X is simple. “Simple“ means that there is no compact subvariety through the very general point of X and X not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical bundle is not nef, admits a contraction unless X is simple with Kodaira dimension - ∞ .

How to cite

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Peternell, Thomas. "Towards a Mori theory on compact Kähler threefolds III." Bulletin de la Société Mathématique de France 129.3 (2001): 339-356. <http://eudml.org/doc/272301>.

@article{Peternell2001,
abstract = {Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e.$K_X$ is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of $K_X$ is generated by global sections); unless $X$ is simple. “Simple“ means that there is no compact subvariety through the very general point of $X$ and $X$ not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical bundle is not nef, admits a contraction unless $X$ is simple with Kodaira dimension $- \infty .$},
author = {Peternell, Thomas},
journal = {Bulletin de la Société Mathématique de France},
keywords = {kähler threefolds; abundance; rational curves; Kodaira dimension},
language = {eng},
number = {3},
pages = {339-356},
publisher = {Société mathématique de France},
title = {Towards a Mori theory on compact Kähler threefolds III},
url = {http://eudml.org/doc/272301},
volume = {129},
year = {2001},
}

TY - JOUR
AU - Peternell, Thomas
TI - Towards a Mori theory on compact Kähler threefolds III
JO - Bulletin de la Société Mathématique de France
PY - 2001
PB - Société mathématique de France
VL - 129
IS - 3
SP - 339
EP - 356
AB - Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e.$K_X$ is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of $K_X$ is generated by global sections); unless $X$ is simple. “Simple“ means that there is no compact subvariety through the very general point of $X$ and $X$ not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical bundle is not nef, admits a contraction unless $X$ is simple with Kodaira dimension $- \infty .$
LA - eng
KW - kähler threefolds; abundance; rational curves; Kodaira dimension
UR - http://eudml.org/doc/272301
ER -

References

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