Journal of the European Mathematical Society
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Published online: 2007-12-31
Corrigendum: A construction of the Deligne–Mumford orbifold (J. Eur. Math. Soc. 8, 611–699 (2006))
Joel W. Robbin[1] and Dietmar A. Salamon[2] (1) University of Wisconsin, Madison, USA(2) ETH Zürich, Switzerland
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 α=0. When the genus is 0 or 1 and in addition α≠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 α=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].
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Robbin Joel, Salamon Dietmar: Corrigendum: A construction of the Deligne–Mumford orbifold (J. Eur. Math. Soc. 8, 611–699 (2006)). J. Eur. Math. Soc. 9 (2007), 901-905. doi: 10.4171/JEMS/101