Pinaki Mondal (Weizmann Institute): A calculus to determine algebraicity of surfaces
Vortrag im Rahmen des Seminars “Algebra und Geometrie”
Abstract: It is a classical problem of complex analytic geometry to determine when a given analytic space has an algebraic structure. For nonsingular surfaces the solution is given by the Enriques-Kodaira classification. For singular surfaces, however we only have some sufficiency results (due to Grauert, Artin, Brenton and others) and the general picture is not clear.
In this talk we present a new (and effective) algebraicity criterion for a class of surfaces containing the complex plane (C^2). We will also talk about some applications, in particular, a joint work with Tim Netzer on the classical “moment problem”, which asks, given a closed subset S of R^n, for characterization of linear functionals on the ring of polynomials(over R) which arise from integration on S with respect to some (Borel) measure on S. If time permits, we will also talk about how the criterion leads to the solution of a special case of the Abhyankar-Sathaye conjecture on embeddings of C^2 in C^3.