Hyperbolic algebraic and analytic curves Jim AglerJohn McCarthy 14H1530F10hyperbolicalgebraic curvefinite codimensional sublagebrapetalholomap A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the holomorphic functions on the desingularization. We show that classical analytic techniques, such as interpolation, can be used to answer geometric questions about the existence of biholomorphic maps. Conversely, we show that the algebraic-geometric viewpoint leads to interesting questions in classical analysis. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3263 10.1512/iumj.2007.56.3263 en Indiana Univ. Math. J. 56 (2007) 2899 - 2934 state-of-the-art mathematics http://iumj.org/access/