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arXiv · 1504.01579

Strongly quasi-proper maps and the f-flattening theorem

Daniel Barlet
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Abstract

We complete and precise the results of [B.13] and we prove a strong version of the semi-proper direct image theorem with values in the space C f n (M) of finite type closed n--cycles in a complex space M. We describe the strongly quasi-proper maps as the class of holomorphic surjective maps which admit a meromorphic family of fibers and we prove stability properties of this class. In the Appendix we give a direct and short proof of D. Mathieu's flattening theorem (see [M.00]) for a strongly quasi-proper map which is easier and more accessible.

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Daniel Barlet. 2015-04-07. Strongly quasi-proper maps and the f-flattening theorem. https://arxiv.org/abs/1504.01579

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