A tranversality theorem for holomorphic mappings and stability of Eisenman-Kobayashi measures

@article{Kaliman1996ATT,
  title={A tranversality theorem for holomorphic mappings and stability of Eisenman-Kobayashi measures},
  author={Shulim Kaliman and Mikhail Zaidenberg},
  journal={Transactions of the American Mathematical Society},
  year={1996},
  volume={348},
  pages={661-672}
}
We show that Thom’s Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping f : S → M from a Stein manifold S to a complex manifold M and given an analytic subset A of the jet space Jk(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… Expand
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References

SHOWING 1-10 OF 26 REFERENCES
Moving holomorphic disks off analytic subsets
Holomorphic maps of the unit disk into a complex manifold X, which miss an analytic subset A of codimension > 2, are shown to be dense in all holomorphic maps of the disk into X. This implies thatExpand
Exotic analytic structures and Eisenman intrinsic measures
Using Eisenman intrinsic measures we prove a cancellation theorem. This theorem allows to find new examples of exotic analytic structures onCn under which we understand smooth complex affineExpand
Some remarks on the intrinsic measures of Eisenman
This paper studies the intrinsic measures on complex manifolds first introduced by Eisenman in analogy with the intrinsic distances of Kobayashi. Some standard conjectures, together with several newExpand
Complex Analytic Sets
The theory of complex analytic sets is part of the modern geometric theory of functions of several complex variables. Traditionally, the presentation of the foundations of the theory of analytic setsExpand
Algebraic approximations of holomorphic maps from Stein domains to projective manifolds
It is shown that every holomorphic map $f$ from a Runge domain $\Omega$ of an affine algebraic variety $S$ into a projective algebraic manifold $X$ is a uniform limit of Nash algebraic maps $f_\nu$Expand
Singularties of differentiable maps
© Publications mathématiques de l’I.H.É.S., 1967, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
...
1
2
3
...