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The singularity category of a Nakayama algebra

Let $A$ be a Nakayama algebra. We give a description of the singularity category of $A$ inside its stable module category. We prove that there is a duality between the singularity category of $A$ and the singularity category of its opposite algebra. As a consequence, the resolution quiver of $A$ and the resolution quiver of its opposite algebra have the same number of cycles and the same number of cyclic vertices.