Valuative analysis of planar plurisubharmonic functions
dc.contributor.author | Favre, Charles | en_US |
dc.contributor.author | Jonsson, Mattias | en_US |
dc.date.accessioned | 2006-09-11T17:58:12Z | |
dc.date.available | 2006-09-11T17:58:12Z | |
dc.date.issued | 2005-11 | en_US |
dc.identifier.citation | Favre, Charles; Jonsson, Mattias; (2005). "Valuative analysis of planar plurisubharmonic functions." Inventiones mathematicae 162(2): 271-311. <http://hdl.handle.net/2027.42/46593> | en_US |
dc.identifier.issn | 0020-9910 | en_US |
dc.identifier.issn | 1432-1297 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46593 | |
dc.description.abstract | We show that valuations on the ring R of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions, giving rise to generalized Lelong numbers in the sense of Demailly. Any plurisubharmonic function thus defines a real-valued function on the set of valuations on R and – by way of a natural Laplace operator defined in terms of the tree structure on – a positive measure on . This measure contains a great deal of information on the singularity at the origin. Under mild regularity assumptions, it yields an exact formula for the mixed Monge-Ampère mass of two plurisubharmonic functions. As a consequence, any generalized Lelong number can be interpreted as an average of valuations. Using our machinery we also show that the singularity of any positive closed (1,1) current T can be attenuated in the following sense: there exists a finite composition of blowups such that the pull-back of T decomposes into two parts, the first associated to a divisor with normal crossing support, the second having small Lelong numbers. | en_US |
dc.format.extent | 622858 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Mathematics, General | en_US |
dc.title | Valuative analysis of planar plurisubharmonic functions | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1109, USA; Department of Mathematics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden | en_US |
dc.contributor.affiliationother | Institut de Mathématiques, Equipe Géométrie et Dynamique, CNRS-Université Paris 7, F-75251, Paris Cedex 05, France | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46593/1/222_2005_Article_443.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s00222-005-0443-2 | en_US |
dc.identifier.source | Inventiones mathematicae | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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