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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 for every positive integer big enough.
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Gilberto Bini, Filippo F. Favale, An unbounded family of log Calabi–Yau pairs. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 3, pp. 619–633DOI 10.4171/RLM/779