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Log Canonical Counterexamples to the Chen--Jiang Decomposition
We construct a projective log-smooth surface pair $(X,Δ)$ and a morphism $f:X\to E$ to an elliptic curve such that $f_*\OO_X(K_X+Δ)$ is Atiyah's indecomposable rank-two bundle $F_2$ of degree zero. This gives a negative answer to Question 3.4 of Jiang \cite{Jiang}. We also construct a log canonical
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