ag.algebraic geometry – Correct reference for a proposal in an article by Kapranov-Vasserot

In the article "Kleinian Singularities, Derived Categories and Hall Algebras" Math. Ann. 316 (2000) of Kapranov-Vasserot, the authors write on page 569 that the complex $ mathcal {L} & # 39; $ (defined on p.568) is almost isomorphic to the spray of structure $ mathcal {O} _ { Delta} $. The reference given to this effect is the article by C.M. Ringel, "Hall algebras and quantum groups", Invent. Math. 101 (1990) and in particular Lemma 4.10. However, I am unable to find such a lemma or even why this is true.

Does anyone know the correct ref. or even better explain why this is true?

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