Irreducible plane curves with the Albanese dimension 2

Tokunaga, Hiro-o

doi:10.1090/S0002-9939-99-05116-3

Irreducible plane curves with the Albanese dimension 2
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Proc. Amer. Math. Soc. 127 (1999), 1935-1940 Request permission

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 $\max _{ n \in {\mathbf {N}}} \left ( \operatorname {dim} \Im (S_{n} \to \operatorname {Alb} (S_{n})) \right )$ 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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