A type of the Lefschetz hyperplane section theorem on \Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities

Abstract

We prove a type of the Lefschetz hyperplane section theorem on Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities by using some degeneration method. As a byproduct, we obtain a new example of a Calabi-Yau 3-fold $X$ with Picard number one whose invariants are $$(H_X^3,c_2(X)\cdot H_X,e(X))=(8,44,-88),$$ where $H_X$, $e(X)$ and $c_2(X)$ are an ample generator of $\Pic(X)$, the topological Euler characteristic number and the second Chern class of $X$ respectively.

arXiv comment9 pages