Calabi-Yau 3-folds of Picard number 2 with hypersurface Cox rings (Q2097299)

A Calabi-Yau variety is a normal projective complex variety \(X\) with at most canonical singularities such that \(K_X\sim 0\) and \(h^i(X, \mathcal{O}_X ) = 0\) for \(0\leq i <\dim X\). The Cox ring of \(X\) is defined by \[ \mathcal{R}(X):=\bigoplus_{[D]\in \text{Cl}(X)}\Gamma(X, D). \] This paper gives a classification of smooth Calabi-Yau \(3\)-folds of Picard number \(2\) such that \(\mathcal{R}(X)\simeq \mathbb{C}[T_1, \dots, T_r]/(g)\) is a general hypersurface Cox ring