Abstract
We address the question “when the local image of a map is well defined” and answer it in case of holomorphic map germs with target $(\mathbb{C}^2, 0)$. We prove a criterion for holomorphic map germs $(X, x) \to (Y, y)$ to be locally open, solving a conjecture by Huckleberry in all dimensions.
Funding Statement
The authors acknowledge the support of the Labex CEMPI (ANR-11-LABX-0007-01). The first author acknowledges the CNCS grant PN-III-P4-ID-PCE-2016-0330.
Citation
Cezar Joiţa. Mihai Tibăr. "The local image problem for complex analytic maps." Ark. Mat. 59 (2) 345 - 358, October 2021. https://doi.org/10.4310/ARKIV.2021.v59.n2.a5
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