Let $X,Y,Z$ be reduced algebraic varieties, and let $Y$ and $Z$ be normal. Let $f:X \to Y$ and $g:X \to Z$ two surjective projective morphisms of algebraic varieties such that the geometric fibers of $f$ and $g$ coincide. Are $f$ and $g$ the same morphism (maybe up to Is there an isomorphism $Y\cong Z$)h:Y\to Z$such that$g=h \circ f$? 5 deleted 4 characters in body Let$X,Y,Z$be irreducible reduced algebraic varieties, and let$Y$and$Z$be normal. Let$f:X \to Y$and$g:X \to Z$two projective morphisms of algebraic varieties such that the geometric fibers of$f$and$g$coincide. Are$f$and$g$the same morphism (maybe up to an isomorphism$Y\cong Z$)? 4 deleted 36 characters in body Let$X,Y,Z$be irreducible algebraic varieties, and let$Y$and$Z$be normal. Let$f:X \to Y$and$g:X \to Z$two projective morphisms of algebraic varieties such that$Y$and$Z$coincide set-theoretically, and such that the geometric fibers of$f$and$g$coincideas varieties. Are$f$and$g$the same morphism (maybe up to an isomorphism$Y\cong Z\$)?