複素代数多様体の双有理不変数について

概要

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In this paper, we study properties of some birational invariants of a complex variety and a fibred space to classify complex algebraic varieties (resp. Kaehlerian manifolds) into the following three types (i) hyperbolic type (ii) parabolic type (iii) elliptic type. ln §1, we define Kodaira and weak Kodaira dimensions and the concepts of pseudo-effectivity, semipositivity and universal effectivity for a coherent sheaf. ln §2, we prove three elementary properties (i) functoriality (ii) easy addition theorem (iii) parabolicity theorem for a weak canonical fibering. ln §3,we prove one of Sakai's conjectures forλ-dimensions under some assumption. Moreover, we consider a deformation theory of complete complex algebraic structures (resp. compact Kaehlerian structures) up to birational equivalence (resp. bimeromorphic equivalence).
東京工芸大学の論文