國立清華大學 數學系

Abstract Mistretta and Urbinati generalized the notion of the Iitaka dimension to vector bundles on a projective variety. Since there is no general framework for discussing the Iitaka dimension \kappa(X,E) of a vector bundle E, some of the most fundamental questions still remain open. For example, there is still no concrete example such that \kappa(X,E)<\kappa(X,\det E). In this talk, first we will discuss the case \dim X=1, showing that the relevant invariants behave quite nicely under the assumption. Then we will talk about the Iitaka dimension of a toric vector bundle on a smooth complete toric variety. We will demonstrate how to translate things to combinatorial language, and how to construct examples with required properties.