Corrigendum: A construction of the Deligne–Mumford orbifold (J. Eur. Math. Soc. 8, 611–699 (2006))

Abstract

We correct an error in [3, Lemma 8.2]. As stated, the lemma only holds for surfaces of genus greater than $1$ or in the case $\alpha =0$. When the genus is $0$ or $1$ and in addition $\alpha \ne 0$, equation (2) in [3] (in the present corrigendum this is equation (2)) is only a necessary condition for the integrability of $J$ but is not sufficient. In [3] Lemma 8.2 is only used twice. On page 637 it is used in the trivial case $\alpha =0$. On page 642 only the “only if” direction is used and the proof of that direction is correct in [3]. In this note we prove a corrected version of [3, Lemma 8.2].

Link to the paper corrected hereby.