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Local deformations of isolated singularities associated with negative line bundles over abelian varieties

Published online by Cambridge University Press:  22 January 2016

Hideo Omoto  and
Shigeo Nakano
Hideo Omoto
Affiliation:
Nagoya University and Kyoto University
Shigeo Nakano
Affiliation:
Nagoya University and Kyoto University
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Let V be an analytic space with an isolated singularity p. In [1] M. Kuranishi approached the problem of deformations of isolated singularities (c.f. [2] and [3]) as follows; Let M be a real hypersurface in the complex manifold V − {p}. Then one has the induced CR-structure °T″(M) on M by the inclusion map i: M→ V − {p} (c.f. Def. 1.6). Then deformations of the isolated singularity (V, p) give rise to ones of the induced CR-structure °T″(M). He established in §9 in [1] the universality theorem for deformations of the induced CR-structure °T″(M)9 when M is compact strongly pseudo-convex (Def. 1.5) of dim M ≧ 5. Form this theorem we can know CR-structures on M which appear in deformations of °T″(M).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 75 , September 1979 , pp. 41 - 70
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Kuranishi, M., Deformations of isolated singularities and ∂̅b , Preprint, Columbia Univ. (1973).Google Scholar
[2] Schlessinger, M., On rigid singularities, Rice Univ. Studies 59 (1973), 147–162.Google Scholar
[3] Tjurina, G. N., Locally semiuniversal flat deformations of isolated singularities of complex spaces, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1970), 1026–1058.Google Scholar
[4] Akahori, T., Intrinsic formula for Kuranishi’s, to appear in Publications Res. Inst. Math. Sciences, Kyoto Univ.Google Scholar
[5] Weil, A., Variétés Kahlériennes, Hermann, Paris, (1958).Google Scholar
[6] Grauert, H., Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368.Google Scholar