Chebyshev constants and transfinite diameter on algebraic curves in $\mathbb{C}^2$ S. Ma'u 14Q0532U20algebraic curveChebyshev constanttransfinite diameterVandermonde determinant Directional Chebyshev constants and transfinite diameter are defined for compact subsets of a complex algebraic curve in $\mathbb{C}^2$. Given such a compact subset $K$, a formula equating the geometric mean of the directional Chebyshev constants of $K$ with its transfinite diameter is proved. This formula generalizes the relation between the classical transfinite diameter and Chebyshev constant in the complex plane, and is a discrete analog of Zaharjuta's integral formula for the Fekete-Leja transfinite diameter in $\mathbb{C}^n$. Further properties of the Chebyshev constants and transfinite diameter are also studied. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4400 10.1512/iumj.2011.60.4400 en Indiana Univ. Math. J. 60 (2011) 1767 - 1796 state-of-the-art mathematics http://iumj.org/access/