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Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
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Ehresmann's without properness in the algebraic category?
Ehresmann's theorem for manifolds states: If $f : X \to Y$ is a proper submersion, then $X$ is a locally trivial fibration on $Y$.
Some sources I am reading (Lazarsfeld Positivity in Algebraic Geomet …