國立清華大學 數學系

Abstract One most fundamental family of birational invariants of a projective manifold is formed by the spaces of pluricanonical forms on the manifold. On each of these "pluricanonical spaces" is defined canonically a norm-like function, called the pseudonorm. The pseudonormed pluricanonical spaces themselves are still birational invariants. Inspired by Royden's work on isometries between spaces of quadratic differentials of compact Riemann surfaces, S.-T. Yau proposed to study possible generalization in birational geometry for higher dimensions. Around a decade ago, based on the support of some positive results obtained in my thesis, Yau proposed an approach towards the birational classification of algebraic varieties, which I will refer to as the pseudonorm project. I will talk on the developments so far since Royden's result along this direction.