An unbounded family of log Calabi–Yau pairs

Abstract

We give an explicit example of log Calabi–Yau pairs that are log canonical and have a linearly decreasing Euler characteristic. This is constructed in terms of a degree two covering of a sequence of blow ups of three dimensional projective bundles over the Segre–Hirzebruch surfaces ${\mathbb{F}}_n$ for every positive integer $n$ big enough.