A new bound on the number of special fibers in a pencil of curves

Author:
S. Yuzvinsky

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1641-1648

MSC (2000):
Primary 14H50; Secondary 32S22, 52C35

Published electronically:
November 19, 2008

MathSciNet review:
2470822

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Abstract | References | Similar Articles | Additional Information

Abstract: In a paper by J. V. Pereira and the author it was proved that any pencil of plane curves of degree 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 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:
yuz@uoregon.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09753-0

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

Article copyright:
© Copyright 2008
American Mathematical Society