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Analyticity of sets associated to Lelong numbers and the extension of meromorphic maps. (English) Zbl 0282.32006


MSC:

32C30 Integration on analytic sets and spaces, currents
32D15 Continuation of analytic objects in several complex variables
32H99 Holomorphic mappings and correspondences
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C65 Integral geometry
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[1] Errett Bishop, Conditions for the analyticity of certain sets, Michigan Math. J. 11 (1964), 289 – 304. · Zbl 0143.30302
[2] Enrico Bombieri, Algebraic values of meromorphic maps, Invent. Math. 10 (1970), 267 – 287. · Zbl 0214.33702 · doi:10.1007/BF01418775
[3] Enrico Bombieri, Addendum to my paper: ”Algebraic values of meromorphic maps” (Invent. Math. 10 (1970), 267 – 287), Invent. Math. 11 (1970), 163 – 166. · doi:10.1007/BF01404610
[4] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. · Zbl 0176.00801
[5] Phillip A. Griffiths, Two theorems on extensions of holomorphic mappings, Invent. Math. 14 (1971), 27 – 62. · Zbl 0223.32016 · doi:10.1007/BF01418742
[6] F. R. Harvey and James R. King, On the structure of positive currents, Invent. Math. 15 (1972), 47 – 52. · Zbl 0235.32006 · doi:10.1007/BF01418641
[7] James R. King, The currents defined by analytic varieties, Acta Math. 127 (1971), no. 3-4, 185 – 220. · Zbl 0224.32008 · doi:10.1007/BF02392053
[8] P. Lelong, Plurisubharmonic functions and positive differential forms, Gordon and Breach, New York, 1969. MR 39 #4436. · Zbl 0195.11604
[9] Bernard Shiffman, Extension of positive line bundles and meromorphic maps, Invent. Math. 15 (1972), no. 4, 332 – 347. · Zbl 0223.32017 · doi:10.1007/BF01405087
[10] Yum Tong Siu, A Thullen type extension theorem for positive holomorphic vector bundles, Bull. Amer. Math. Soc. 78 (1972), 775 – 776. · Zbl 0253.32016
[11] Henri Skoda, Sous-ensembles analytiques d’ordre fini ou infini dans \?\(^{n}\), Bull. Soc. Math. France 100 (1972), 353 – 408 (French). · Zbl 0246.32009
[12] Paul R. Thie, The Lelong number of a point of a complex analytic set, Math. Ann. 172 (1967), 269 – 312. · Zbl 0158.32804 · doi:10.1007/BF01351593
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