# Aggressive geometry – Non-flat locus for smooth patterns

Let $$X$$, $$Y$$ to be connected smooth patterns of finite type on an algebraically closed characteristic field $$0$$. Let $$f: X rightarrow Y$$ to be a surjective non-birational morphism on the underlying topological spaces. Can the non-flat locus of $$f$$ to be non-empty of codimension$$geq 2$$ in $$X$$? For birational morphism, I think that ZMT plus a purity theorem show that the answer is "no".

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