title: A geometric approach to problems in birational geometry.
abstract: 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 that 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.
authors.affiliation: Department of Mathematics, Harvard University, Cambridge, MA 02138, USA. cychi@math.harvard.edu
authors.forename: Chen-Yu
authors.initials: CY
authors.lastname: Chi
authors.forename: Shing-Tung
authors.initials: ST
authors.lastname: Yau
mesh_terms: D000465:Algorithms; D008433:Mathematics; D015233:Models, Statistical