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We provide a complete classification of hexagonal singular 3-web germs in thecomplex plane, satisfying the following two conditions: 1) the Chern connectionremains holomorphic at the singular point, 2) the web admits at least oneinfinitesimal symmetry at this point. As a by-product, a classification ofhexagonal weighted homogeneous 3-webs is obtained.

Local classification of singular hexagonal 3-webs with holomorphic Chern connection and infinitesimal symmetries