Normal Compactifications of the complex plane
Toronto University, Canada.
Abstract: We describe a newly observed correspondence between two well studied objects: planar complex algebraic curves with one place at infinity (studied e.g. by Abhyankar-Moh (1975), Russell (1980), Nakazawa-Oka (1997), Suzuki(1999)) and normal algebraic compactifications of the complex plane with one curve at infinity (studied e.g. by Kojima (2001), Kojima-Takahashi (2009)). This result leads to a classification of normal analytic compactifications of the complex plane with one curve at infinity, and gives an effective criterion for determining when the result of contracting certain negative definite rational curves from a rational algebraic surface is also algebraic. In particular, it gives an effective algorithm to construct non-algebraic normal analytic surfaces.