On classification of Q-Fano 3-folds with Gorenstein index 2 and Fano index 1/2

Abstract

We obtain a classification of a Q-factorial Q-Fano 3-fold $X$ with the following properties: the Picard number of $X$ is 1; the Gorenstein index of $X$ is 2; the Fano index of $X$ is 1/2; $h^0(-K_X)\ge 4$; there exists an index 2 point $P$ such that $(X,P)\simeq (\{xy+f(z^2,u)=0\}/{\mathbb{Z}}_2(1,1,1,0),o)$ with $ordf(Z,U)=1$.

References in corpus (2)

• Deformations of Q-Calabi-Yau 3-folds and Q-Fano 3-folds of Fano index 1
• Effective base point freeness on normal surfaces