A Note on Tsuji’s Criterion for Numerical Triviality

Shigetaka Fukuda,Li Guo

doi:10.1155/2022/6304862

Abstract

In this study, we give an alternative and elementary proof to Tsuji’s criterion for a Cartier divisor to be numerically trivial.

Highlights

In this article, every algebraic variety is proper over the field of complex numbers C.In 1970s, Iitaka [1] initiated the classification theory of higher dimensional algebraic varieties by using the pluricanonical systems
In the statement of Lemma 1, condition (1) immediately implies that L is numerically trivial on every general fiber of the morphism f by considering the flattening
We prove the assertion by induction on

Summary

Introduction

Every algebraic variety is proper over the field of complex numbers C.In 1970s, Iitaka [1] initiated the classification theory of higher dimensional algebraic varieties by using the pluricanonical systems. In the statement of Lemma 1, condition (1) immediately implies that L is numerically trivial on every general fiber of the morphism f by considering the flattening. (4) g is a morphism with only connected fibers ere exists some irreducible component W′ of μ−1(W), such that g(W′) B′.

Results

Conclusion