Limits of multipole pluricomplex Green functions
| Autor: | Alexander Rashkovskii, Ragnar Sigurdsson, Jón Magnússon, Pascal J. Thomas |
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| Přispěvatelé: | Science Institute, University of Iceland [Reykjavik], Faculty of Science and Technology, University of Stavanger, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Partenariats Hubert Curien 'Jules Verne' in 2006-2007 (12339SE) and in 2008-2009 (18980ZB), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
General Mathematics Uniform convergence Complete intersection MSC 32U35 32A27 01 natural sciences Mathematics - Algebraic Geometry ideals of analytic functions Monge Ampère operator 0103 physical sciences FOS: Mathematics 0101 mathematics Complex Variables (math.CV) Algebraic Geometry (math.AG) Mathematics Mathematics::Commutative Algebra Mathematics - Complex Variables 010102 general mathematics Multiplicity (mathematics) [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] Codimension Vanishing ideal Bounded function pluricomplex Green function 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Multipole expansion 32U35 32A27 |
| Zdroj: | International Journal of Mathematics International Journal of Mathematics, World Scientific Publishing, 2012, 23 (6), pp.1250065. ⟨10.1142/S0129167X12500656⟩ International Journal of Mathematics, 2012, 23 (6), pp.1250065. ⟨10.1142/S0129167X12500656⟩ |
| ISSN: | 0129-167X 1793-6519 |
| Popis: | Let $S_\epsilon$ be a set of $N$ points in a bounded hyperconvex domain in $C^n$, all tending to 0 as$\epsilon$ tends to 0. To each set $S_\epsilon$ we associate its vanishing ideal $I_\epsilon$ and the pluricomplex Green function $G_\epsilon$ with poles on the set. Suppose that, as $\epsilon$ tends to 0, the vanishing ideals converge to $I$ (local uniform convergence, or equivalently convergence in the Douady space), and that $G_\epsilon$ converges to $G$, locally uniformly away from the origin; then the length (i.e. codimension) of $I$ is equal to $N$ and $G \ge G_I$. If the Hilbert-Samuel multiplicity of $I$ is strictly larger than $N$, then $G_\epsilon$ cannot converge to $G_I$. Conversely, if the Hilbert-Samuel multiplicity of $I$ is equal to $N$, (we say that $I$ is a complete intersection ideal), then $G_\epsilon$ does converge to $G_I$. We work out the case of three poles; when the directions defined by any two of the three points converge to limits which don't all coincide, there is convergence, but $G > G_I$. Comment: 41 p., version 2. A section linking our notion of convergence to the topology of the Douady space has been added. Some typos have been corrected |
| Databáze: | OpenAIRE |
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