Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-14T23:19:01.416Z Has data issue: false hasContentIssue false
  • English
  • Français

Elliptic ruled surfaces on Calabi–Yau threefolds

Published online by Cambridge University Press:  24 October 2008

P. M. H. Wilson
P. M. H. Wilson
Affiliation:
Department of Pure Mathematics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB
Get access Rights & Permissions [Opens in a new window]

Extract

In [5], we studied the behaviour of the Kähler cone of Calabi–Yau threefolds under deformations. We saw that the Kähler cone is locally constant in a smooth family of Calabi–Yau threefolds, unless some of the threefolds Xb contain elliptic ruled surfaces. Moreover, if X is a Calabi–Yau threefold containing an elliptic ruled surface, then the Kähler cone is not invariant under a generic small deformation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 45 - 52
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Brieskorn, E.. Die Auflösung der rationalen Singularitäten holomorpher Abbildungen. Math. Ann. 178 (1968), 255–270.CrossRefGoogle Scholar
[2]Burns, D. and Rapoport, M.. On the Torelli Problem for Kählerian K-3 surfaces. Ann. Scient. École Norm. Sup. (4), 8 (1975), 235–274.Google Scholar
[3]Reid, M.. Minimal models of canonical 3-folds. In Algebraic Varieties and Analytic Varieties (ed. Iitaka, S.). Advanced Studies in Pure Math. vol. 1 (Kinokuniya and North Holland, 1983), pp. 395–418.Google Scholar
[4]Wilson, P. M. H.. Calabi-Yau manifolds with large Picard number. Invent. Math. 98 (1989), 139–155.CrossRefGoogle Scholar
[5]Wilson, P. M. H.. The Kähler cone on Calabi–Yau threefolds. Invent. Math. 107 (1992), 561–583.Google Scholar