Pseudonorms and theorems of Torelli type for birational equivalence.

摘要

Our research interest has been in the birational classification of complex projective varieties using invariants. A classical set of birational invariants of a variety M are the pluricanonical spaces H 0(M, mKM) 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? We are able to give a positive answer to this question for varieties of general type. Our results can be thought of as theorems of Torelli type for birational equivalence.