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Lelong classes of plurisubharmonic functions on an affine variety (1806.10780v1)
Published 28 Jun 2018 in math.CV
Abstract: We study the Lelong classes $\mathcal{L}(V),\mathcal{L}+(V)$ of psh functions on an affine variety $V$. We compute the Monge-Amp`ere 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 B\'ezout's theorem.
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