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On a question of Miles Reid

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Abstract:

A conjecture of Miles Reid states that the relative canonical algebra for a pencil of curves of genus greater than one is always generated in degrees at most three (1-2-3 conjecture). We give some explicit counter-examples to the conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Osaka University, 1–16 Machikaneyama, Toyonaka Osaka 560-0043, Japan.¶E-mail: konno@math.wani.osaka-u.ac.jp, , , , , , JP

    Kazuhiro Konno

  2. Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal. E-mail: mmlopes@lmc.fc.ul.pt, , , , , , PT

    Margarida Mendes Lopes

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  1. Kazuhiro Konno
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  2. Margarida Mendes Lopes
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Received: 10 December 1998/ Revised version: 15 April 1999

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Konno, K., Mendes Lopes, M. On a question of Miles Reid. manuscripta math. 100, 81–86 (1999). https://doi.org/10.1007/s002290050196

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  • DOI: https://doi.org/10.1007/s002290050196

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