Arkiv för Matematik

Residue calculus for c-holomorphic functions

Maciej P. Denkowski

Full-text: Open access

Abstract

In this paper we introduce Coleff–Herrera residue currents defined by systems of c-holomorphic functions and prove a Lelong–Poincaré and a Cauchy-type formula as well as the transformation law for these currents.

Article information

Source
Ark. Mat., Volume 47, Number 1 (2009), 73-89.

Dates
Received: 8 May 2006
Revised: 14 April 2008
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907067

Digital Object Identifier
doi:10.1007/s11512-008-0088-7

Mathematical Reviews number (MathSciNet)
MR2480916

Zentralblatt MATH identifier
1183.32008

Rights
2008 © Institut Mittag-Leffler

Citation

Denkowski, Maciej P. Residue calculus for c-holomorphic functions. Ark. Mat. 47 (2009), no. 1, 73--89. doi:10.1007/s11512-008-0088-7. https://projecteuclid.org/euclid.afm/1485907067


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References

  • Berenstein, C. A., Vidras, A. and Yger, A., Analytic residues along algebraic cycles, J. Complexity 21 (2005), 5–42.
  • Chirka, E. M., Complex Analytic Sets, Mathematics and its Applications (Soviet Series) 46, Kluwer, Dordrecht, 1989.
  • Coleff, N. R. and Herrera, M. E., Les courants résiduels associés à une forme méromorphe, Lecture Notes in Mathematics 633, Springer, Berlin–Heidelberg, 1978.
  • Demailly, J. P., Courants positifs et théorie de l’intersection, Gaz. Math. 53 (1992), 131–159.
  • Denkowski, M. P., A note on the Nullstellensatz for c-holomorphic functions, Ann. Polon. Math. 90 (2007), 219–228.
  • Draper, R. N., Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175–204.
  • Henkin, G. and Passare, M., Abelian differentials on singular varieties and variations on a theorem of Lie–Griffiths, Invent. Math. 135 (1999), 297–328.
  • Remmert, R., Projektionen analytischer Mengen, Math. Ann. 130 (1956), 410–441.
  • Shcherbina, N., Pluripolar graphs are holomorphic, Acta Math. 194 (2005), 203–216.
  • Tsikh, A. K., Multidimensional Residues and their Applications, Translations of Mathematical Monographs 103, Amer. Math. Soc., Providence, RI, 1992.
  • Tsikh, A. and Yger, A., Residue currents, J. Math. Sci. (N. Y.) 120:6 (2004), 1916–1971.
  • Whitney, H., Complex Analytic Varieties, Addison-Wesley, Reading–London–Don Mills, 1972.