Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Semiglobal results for $\overline\partial$ on a complex space with arbitrary singularities


Authors: John Erik Fornæss, Nils Øvrelid and Sophia Vassiliadou
Journal: Proc. Amer. Math. Soc. 133 (2005), 2377-2386
MSC (2000): Primary 32B10, 32J25, 32W05, 14C30
Published electronically: March 22, 2005
MathSciNet review: 2138880
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. J.M. Aroca, H. Hironaka and J.L. Vicente, Desingularization theorems, Mem. Math. Inst. Jorge Juan, No. 30, Madrid, 1977.
  • 2. 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, 10.1007/s002220050141
  • 3. Klas Diederich, John Erik Fornæss, and Sophia Vassiliadou, Local 𝐿² results for \overline∂ on a singular surface, Math. Scand. 92 (2003), no. 2, 269–294. MR 1973947
  • 4. John Erik Fornæss, 𝐿² results for \overline∂ in a conic, Complex analysis and related topics (Cuernavaca, 1996) Oper. Theory Adv. Appl., vol. 114, Birkhäuser, Basel, 2000, pp. 67–72. MR 1748002
  • 5. Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 0137127
  • 6. Hans Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Inst. Hautes Études Sci. Publ. Math. 5 (1960), 64 (German). MR 0121814
  • 7. 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
  • 8. Robert C. Gunning, Introduction to holomorphic functions of several variables. Vol. III, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1990. Homological theory. MR 1059457
  • 9. Lars Hörmander, 𝐿² estimates and existence theorems for the ∂ operator, Acta Math. 113 (1965), 89–152. MR 0179443
  • 10. S. Łojasiewicz, Sur le problème de la division, Studia Math. 18 (1959), 87–136 (French). MR 0107168
  • 11. B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575
  • 12. Yum-tong Siu, Analytic sheaf cohomology groups of dimension 𝑛 of 𝑛-dimensional noncompact complex manifolds, Pacific J. Math. 28 (1969), 407–411. MR 0243116

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32B10, 32J25, 32W05, 14C30

Retrieve articles in all journals with MSC (2000): 32B10, 32J25, 32W05, 14C30


Additional Information

John Erik Fornæss
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
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

DOI: https://doi.org/10.1090/S0002-9939-05-07963-3
Keywords: Cauchy-Riemann equation, singularity, cohomology groups
Received by editor(s): March 19, 2004
Published electronically: March 22, 2005
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2005 American Mathematical Society