Classification of bi-polarized 3-folds $(X, L_{1}, L_{2})$ with $h^{0}(K_{X}+L_{1}+L_{2})=1$

Abstract

Let $X$ be a complex smooth projective variety of dimension 3, and let $L_1$ and $L_2$ be ample line bundles on $X$. In this paper we classify $(X, L_{1}, L_{2})$ with $h^{0}(K_{X}+L_{1}+L_{2})=1$.