  A classical set of birational invariants of a variety are its spaces of
pluricanonical forms and some of their canonically defined subspaces. Each of
these vector spaces admits a typical metric structure which is also
birationally invariant. These vector spaces so metrized will be referred to as
the pseudonormed spaces of the original varieties. A fundamental question is
the following: given two mildly singular projective varieties with some of the
first variety's pseudonormed spaces being isometric to the corresponding ones
of the second variety's, can one construct a birational map between them which
induces these isometries? In this work a positive answer to this question is
given for varieties of general type. This can be thought of as a theorem of
Torelli type for birational equivalence.
