Global invariants for strongly pseudoconvex varieties with isolated singularities: Bergman functions

Abstract. Let X 1 and X 2 be two compact strongly pseudoconvex CR manifolds of dimension 2n − 1 ≥ 5 which bound complex varieties V 1 and V 2 with only isolated normal singularities in C N 1 and C N 2 respectively. Let S 1 and S 2 be the singular sets of V 1 and V 2 respectively and assume S 2 is non-empty. If 2n − N 2 − 1 ≥ 1 and the cardinality of S 1 is less than twice that of S 2 , then we prove that any non-constant CR morphism from X 1 to X 2 is necessarily a CR biholomorphism. On the other hand, let X be a compact strongly pseudoconvex CR manifold of dimension 3 which bounds a complex variety V with only isolated normal non-quotient singularities. Assume that the singular set of V is non-empty. Then we prove that any non-constant CR morphism from X to X is necessarily a CR biholomorphism.

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Higher order Bergman functions and explicit construction of moduli space for complete Reinhardt domains

Du¹,

Yau²

2009

J. Differential Geom.

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Global invariants for strongly pseudoconvex varieties with isolated singularities: Bergman functions

Cited by 3 publications

References 9 publications

Interplay Between CR Geometry and Algebraic Geometry

Interplay Between CR Geometry and Algebraic Geometry

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Higher order Bergman functions and explicit construction of moduli space for complete Reinhardt domains

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