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We answer an open question concerning the boundedness of canonical fiber spaces in high dimensions and prove the following: for any set of integers    n  ⩾  3   ,and    N  &gt;  0   , there exists a nonsingular projective   n  ‐fold   X   of general type so that   X   is canonically fibered by   d  ‐dimensional varieties   F   withp  g    (  F  )   ⩾  N   . This disproves the desired boundedness parallel to Beauville's boundedness theorem [‘L'application canonique pour les surfaces de type général’,  Invent. Math . 55 (1979) 121–140] in the surface case.

Unboundedness of fiber invariants of canonically fibered varieties of general type