Semiglobal results for $\overline \partial$ on a complex space with arbitrary singularities
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- by John Erik Fornæss, Nils Øvrelid and Sophia Vassiliadou
- Proc. Amer. Math. Soc. 133 (2005), 2377-2386
- DOI: https://doi.org/10.1090/S0002-9939-05-07963-3
- Published electronically: March 22, 2005
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Abstract:
We obtain some $L^2$-results for the $\overline \partial$ operator on forms that vanish to high order on the singular set of a complex space.References
- J.M. Aroca, H. Hironaka and J.L. Vicente, Desingularization theorems, Mem. Math. Inst. Jorge Juan, No. 30, Madrid, 1977.
- Edward Bierstone and Pierre D. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128 (1997), no. 2, 207–302. MR 1440306, DOI 10.1007/s002220050141
- Klas Diederich, John Erik Fornæss, and Sophia Vassiliadou, Local $L^2$ results for $\overline \partial$ on a singular surface, Math. Scand. 92 (2003), no. 2, 269–294. MR 1973947, DOI 10.7146/math.scand.a-14405
- John Erik Fornæss, $L^2$ results for $\overline \partial$ in a conic, Complex analysis and related topics (Cuernavaca, 1996) Oper. Theory Adv. Appl., vol. 114, Birkhäuser, Basel, 2000, pp. 67–72. MR 1748002
- Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
- Hans Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Inst. Hautes Études Sci. Publ. Math. 5 (1960), 64 (German). MR 121814
- Hans Grauert and Reinhold Remmert, Coherent analytic sheaves, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 265, Springer-Verlag, Berlin, 1984. MR 755331, DOI 10.1007/978-3-642-69582-7
- Robert C. Gunning, Introduction to holomorphic functions of several variables. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990. Function theory. MR 1052649
- Lars Hörmander, $L^{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152. MR 179443, DOI 10.1007/BF02391775
- S. Łojasiewicz, Sur le problème de la division, Studia Math. 18 (1959), 87–136 (French). MR 107168, DOI 10.4064/sm-18-1-87-136
- B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, vol. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575
- Yum-tong Siu, Analytic sheaf cohomology groups of dimension $n$ of $n$-dimensional noncompact complex manifolds, Pacific J. Math. 28 (1969), 407–411. MR 243116
Bibliographic Information
- John Erik Fornæss
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
- MR Author ID: 68145
- Email: fornaess@umich.edu
- Nils Øvrelid
- Affiliation: Department of Mathematics, University of Oslo, P.B 1053 Blindern, Oslo, N-0316 Norway
- Email: nilsov@math.uio.no
- Sophia Vassiliadou
- Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057
- Email: sv46@georgetown.edu
- Received by editor(s): March 19, 2004
- Published electronically: March 22, 2005
- Communicated by: Mei-Chi Shaw
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2377-2386
- MSC (2000): Primary 32B10, 32J25, 32W05, 14C30
- DOI: https://doi.org/10.1090/S0002-9939-05-07963-3
- MathSciNet review: 2138880