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Abstract
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Let
and
be two compact strongly pseudoconvex CR manifolds of dimension
which are boundaries
of complex varieties
and with only isolated
normal singularities in
and
,
respectively. We show that any nonconstant CR morphism from
to
can be extended to a finite holomorphic covering map from
to
in the case
where
has only isolated complete intersection singularities. In particular, there is no
nonconstant CR morphism between the links of two isolated complete intersection
singularities with different embedding codimensions. Finally, using Kohn–Rossi
cohomology, we obtain some sufficient conditions for the nonexistence of CR morphisms
from
to
.
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Dedicate to Professor H. Blaine Lawson
on the occasion of his 80th birthday
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Keywords
strongly pseudoconvex CR manifold, rigidity of CR morphism,
isolated complete intersection singularity, Kohn–Rossi
cohomology
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Mathematical Subject Classification
Primary: 32S20, 32V99
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Milestones
Received: 20 June 2021
Revised: 6 October 2021
Accepted: 5 November 2021
Published: 26 February 2022
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