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Dec 6 at 16:16 comment added Naga Venkata @DanielLitt: Thanks! Thats a very nice counterexample :) However, I am mainly interested in hypersurfaces of degrees 2 and higher.
Dec 6 at 16:12 comment added Daniel Litt How about a hyperplane through $x$? (That said, this is the only counterexample.)
Dec 6 at 16:11 comment added Lazzaro Campeotti If this map is not dominant, then $X$ must be a cone with vertex at $x$.
Dec 6 at 15:34 history asked Naga Venkata CC BY-SA 4.0