A Robin Function for Algebraic Varieties and Applications to Pluripotential Theory

Abstract

The Robin function associated to a compact set K captures information about the asymptotic growth of the logarithmic extremal function associated to K and has found numerous applications within pluripotential theory in CN. Despite its use, an analogous function for affine algebraic varieties has not been described in the literature. The work presented here shows how such a function can be constructed and, supposing only mild geometric conditions, a wealth of classical pluripotential theoretic results can be recovered on an affine algebraic variety. Moreover this thesis de nes special coordinates for an algebraic variety (`Noether presentation') which are particularly suited to studying the class L+(V).