Lelong classes of plurisubharmonic functions on an affine variety

Abstract

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.

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  
Year of Publication
2018
Journal
Dolomites Research Notes on Approximation
Volume
11
Issue Number
4
Start Page
84
Last Page
102
Date Published
11/2018
ISSN Number
2035-6803
Serial Article Number
9
DOI
10.14658/PUPJ-DRNA-2018-4-9
Issue
Section
SpecialIssue4