A Tranversality Theorem for Holomorphic Mappings and Stability of Eisenman-Kobayashi Measures

Kaliman, Sh.; Zaidenberg, M.

doi:10.1090/S0002-9947-96-01482-1

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ISSN 1088-6850(online) ISSN 0002-9947(print)

A Tranversality Theorem
for Holomorphic Mappings and
Stability of Eisenman-Kobayashi Measures

Authors: Sh. Kaliman and M. Zaidenberg
Journal: Trans. Amer. Math. Soc. 348 (1996), 661-672
MSC (1991): Primary 32E10, 32H02, 58C10, 58A35, 58A07
MathSciNet review: 1321580
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Abstract: We show that Thom's Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping $f:S\rightarrow M$ from a Stein manifold $S$ to a complex manifold $M$ and given an analytic subset $A$ of the jet space $J^{k} (S, M), \; f$ can be approximated in neighborhoods of compacts by holomorphic mappings whose $k$ -jet extensions are transversal to $A$ . As an application the stability of Eisenman-Kobayshi intrinsic $k$ -measures with respect to deleting analytic subsets of codimension $>k$ is proven. This is a generalization of the Campbell-Howard-Ochiai-Ogawa theorem on stability of Kobayashi pseudodistances.

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