We study the Lelong classes L(V),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.
Lelong classes of plurisubharmonic functions on an affine variety
Ma‘u S., Hart J. (2018) "Lelong classes of plurisubharmonic functions on an affine variety " Dolomites Research Notes on Approximation, 11(4), 84-102. DOI: 10.14658/PUPJ-DRNA-2018-4-9
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Dolomites Research Notes on Approximation
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