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Constructibility of the set of points where a complex analytic morphism is open

Author: Adam Parusiński
Journal: Proc. Amer. Math. Soc. 117 (1993), 205-211
MSC: Primary 32C15; Secondary 14E40
MathSciNet review: 1139472
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Abstract: Using the local flattening theorem we prove that the set of points where a complex analytic morphism is open (or universally open) is constructible. A similar result is obtained for a morphism of complex algebraic varieties.

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  • [BM] E. Bierstone and P. D. Milman, Uniformization of analytic spaces, J. Amer. Math. Soc. 24 (1989), 801-836. MR 1001853 (91c:32033)
  • [DLS] Z. Denkowska, S. Lojasiewicz, and J. Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 27 (1979), 529-535. MR 581546 (81i:32003)
  • [EGA] A. Grothendieck and J. Dieudonne, Éléments de géométrie algébrique. IV, Inst. Hautes Études Sci. Publ. Math. 32 (1967).
  • [F] G. Fisher, Complex analytic geometry, Lecture Notes in Math., vol. 538, Springer-Verlag, Berlin and Heidelberg, 1976. MR 0430286 (55:3291)
  • [H1] H. Hironaka, Introduction to real analytic sets and real-analytic maps, Instituto "L.Tonelli", Pisa, 1973. MR 0477121 (57:16665)
  • [H2] -, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109-326. MR 0199184 (33:7333)
  • [H3] -, Flattening theorem in complex analytic geometry, Amer. J. Math. 97 (1975), 199-265. MR 0393556 (52:14365)
  • [H-L-T] H. Hironaka, M. Lejeune-Jalabert, and B. Teissier, Platificateur local en géométrie analytique et aplatissement local, Astérisque 7-8 (1973), 441-446. MR 0409884 (53:13636)
  • [Hu] R. Huber, Two questions about open mappings, talk at conference "Reelle algebraische Geometrie" Oberwolfach, June 10-16, 1990.
  • [P] A. Parusiński, Subanalytic functions, preprint MPI/90-58; Trans. Amer. Math. Soc. (to appear). MR 1160156 (94k:32006)
  • [R] M. Raynaud, Flat modules in algebraic geometry, Compositio Math. 24 (1972), 11-31. MR 0302645 (46:1789)

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Keywords: Constructible sets, flattening theorem, universally open
Article copyright: © Copyright 1993 American Mathematical Society

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