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

Kaliman, Sh.; Zaidenberg, M.

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

A Tranversality Theorem for Holomorphic Mappings and Stability of Eisenman-Kobayashi Measures
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by Sh. Kaliman and M. Zaidenberg

Trans. Amer. Math. Soc. 348 (1996), 661-672

DOI: https://doi.org/10.1090/S0002-9947-96-01482-1

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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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