Lelong classes of plurisubharmonic functions on an affine variety

Abstract

We study the Lelong classes $\mathcal{L}(V),{\mathcal{L}}^{+}(V)$ of psh functions on an affine variety $V$. We compute the Monge-Ampère mass of these functions, which we use to define the degree of a polynomial on $V$ in terms of pluripotential theory (the Lelong degree). We compute the Lelong degree explicitly in a specific example. Finally, we derive an affine version of Bézout's theorem.

29 pages, 2 figures