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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new bound on the number of special fibers in a pencil of curves
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by S. Yuzvinsky PDF
Proc. Amer. Math. Soc. 137 (2009), 1641-1648 Request permission


In a paper by J. V. Pereira and the author it was proved that any pencil of plane curves of degree $d>1$ with irreducible generic fiber can have at most five completely reducible fibers although no examples with five such fibers had ever been found. Recently Janis Stipins has proved that if a pencil has a base of $d^2$ points, then it cannot have five completely reducible fibers. In this paper we generalize Stipins’ result to arbitrary pencils. We also include into consideration more general special fibers that are the unions of lines and non-reduced curves. These fibers are important for characteristic varieties of hyperplane complements.
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Additional Information
  • S. Yuzvinsky
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 94703
  • Email:
  • Received by editor(s): January 10, 2008
  • Received by editor(s) in revised form: July 27, 2008
  • Published electronically: November 19, 2008
  • Communicated by: Ted Chinburg
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1641-1648
  • MSC (2000): Primary 14H50; Secondary 32S22, 52C35
  • DOI:
  • MathSciNet review: 2470822