Deformations of Strongly Pseudo-Convex CR Structures and Deformations of Normal Isolated Singularities

1991 ◽  
pp. 200-204 ◽  
Author(s):  
Kimio Miyajima
Keyword(s):  
Isolated Singularities ◽  
Pseudo Convex ◽  
Cr Structures

scholarly journals On Realizations of Families of Strongly Pseudo-Convex CR Structures

1992 ◽  
Vol 15 (1) ◽  
pp. 153-170 ◽  
Author(s):  
Kimio MIYAJIMA
Keyword(s):  
Pseudo Convex ◽  
Cr Structures

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

1979 ◽  
Vol 75 ◽  
pp. 41-70
Author(s):  
Hideo Omoto ◽  
Shigeo Nakano
Keyword(s):  
Complex Manifold ◽  
Real Hypersurface ◽  
Abelian Varieties ◽  
Analytic Space ◽  
Line Bundles ◽  
Isolated Singularity ◽  
Isolated Singularities ◽  
Universality Theorem ◽  
Pseudo Convex ◽  
Local Deformations

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).

A Note on the Analogue of the Bogomolov Type Theorem on Deformations of CR-Structures

1994 ◽  
Vol 37 (1) ◽  
pp. 8-12 ◽  
Author(s):  
Takao Akahori ◽  
Kimio Miyajima
Keyword(s):  
Line Bundle ◽  
Type Theorem ◽  
Strict Sense ◽  
Weak Version ◽  
Cr Manifold ◽  
Canonical Line Bundle ◽  
Pseudo Convex ◽  
Cr Structures

AbstractLet (M, °T″) be a compact strongly pseudo-convex CR-manifold with trivial canonical line bundle. Then, in [A-M2], a weak version of the Bogomolov type theorem for deformations of CR-structures was shown by an analogy of the Tian- Todorov method. In this paper, we show that: in the very strict sense, there is a counterexample.

A SMOOTHNESS OF DEFORMATIONS OF NORMAL STRONGLY PSEUDO-CONVEX CR-STRUCTURES

1998 ◽  
Vol 52 (2) ◽  
pp. 413-438
Author(s):  
Takao AKAHORI ◽  
Kimio MIYAJIMA
Keyword(s):  
Pseudo Convex ◽  
Cr Structures
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