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Irreducible plane curves
with the Albanese dimension 2

Author: Hiro-o Tokunaga
Journal: Proc. Amer. Math. Soc. 127 (1999), 1935-1940
MSC (1991): Primary 14H30; Secondary 14E20
Published electronically: February 18, 1999
MathSciNet review: 1637444
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $B$ be a plane curve given by an equation $F(X_{0}, X_{1}, X_{2}) = 0$, and let $B_{a}$ be the affine plane curve given by $f(x, y) = F(1,x, y) = 0$. Let $S_{n}$ denote a cyclic covering of ${\mathbf{P}}^{2}$ determined by $z^{n} = f(x, y)$. The number $\max _{ n \in {\mathbf{N}}} \left ( \text{\rm dim} \, Im(S_{n} \to Alb (S_{n})) \right )$ is called the Albanese dimension of $B_{a}$. In this article, we shall give examples of $B_{a}$ with the Albanese dimension 2.

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Additional Information

Hiro-o Tokunaga
Affiliation: Department of Mathematics and Information Science, Kochi University, Kochi 780, Japan

Received by editor(s): March 13, 1997
Received by editor(s) in revised form: September 26, 1997
Published electronically: February 18, 1999
Additional Notes: This research was partly supported by the Grant-in-Aid for Encouragement of Young Scientists 09740031 from the Ministry of Education, Science and Culture.
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society