To let $ D subset mathbb {C} ^ k $ be your preferred complex domain.

Suppose we get a correct holomorphic map $ f colon D to mathbb {C} ^ {k + 2} $,

Let us take $ k + 1 $ generic linear functions $ l_i colon mathbb {C} ^ {k + 2} an mathbb {C} $, $ i = 1, lpoints, k + 1 $ and make a linear map $ L colon mathbb {C} ^ {k + 2} an mathbb {C} ^ {k + 1} $ by $ L: = (l_1, ldots, l_ {k + 1}) $,

Is it true that $ L circ f $ is also good? How can you show that?

I understand that mathstackexchange is an appropriate place for that

a question. I just want to leave it here.