✦ LIBER ✦

Errata to the Paper “False Hyperelliptic Surfaces with Section”

✍ Scribed by Yoshifumi Takeda

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 42 KB
Volume: 182
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19961820115

No coin nor oath required. For personal study only.

✦ Synopsis

The proof of Lemma 3.1 in Section 3 is valid only for v = 1. In fact, in the case of v 2 2, the assertion of Corollary 3.3 to the lemma contradicts with the supersingularity. Indeed, this corollary asserted that there exists a nontrivial extension of OC by OC such that its pull-back by the p -t h power of the Frobenius k-morphism does not split for p 5 v and splits for p 2 v. However, since Ext'(Oc,Oc) = H'(C,Oc) and since the Frobenius kmorphism induces the zeromapping on H1 (C, OC), the pull-back by the Frobenius k-morphism of any such extension does split. Thus, in all arguments and assertions in Sections 3 and 4, v should be read as 1. Therefore the problem concerning elliptic fibrations stated in Introduction is still open.

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