Abstract
Let G be a finite Abelian group acting (linearly) on space ℝn and, therefore, on its complexification ℂn, and let W be the real part of the quotient ℂn/G (in the general case, W ≠ ℝn/G). The index of an analytic 1-form on the space W is expressed in terms of the signature of the residue bilinear form on the G-invariant part of the quotient of the space of germs of n-forms on (ℝn, 0) by the subspace of forms divisible by the 1-form under consideration.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
References
W. Ebeling and S. M. Gusein-Zade, Geom. Dedicata, 113:1 (2005), 231–241.
W. Ebeling and S. M. Gusein-Zade, Math. Z., 252:4 (2006), 755–766.
D. Eisenbud and H. Levine, Ann. of Math., 106:1 (1977), 19–38.
G. N. Khimshiashvili, Comm. Acad. Sci. Georgian SSR [in Russian], 85:2 (1977), 309–311.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 2, pp. 78–81, 2018
Original Russian Text Copyright © by S. M. Gusein-Zade and W. Ebeling
The work of the first author (the formulation of the problem and the development of the ingredients of the proof related to the residue pairing) was supported by Russian Science Foundation grant 16-11-10018. The work of the second author was partially supported by DFG.
Rights and permissions
About this article
Cite this article
Gusein-Zade, S.M., Ebeling, W. The Index of a 1-Form on a Real Quotient Singularity. Funct Anal Its Appl 52, 144–146 (2018). https://doi.org/10.1007/s10688-018-0220-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10688-018-0220-9