Abstract
We study the analog of the classical infinitesimal center problem in the plane, but for zero cycles. We define the displacement function in this context and prove that it is identically zero if and only if the deformation has a composition factor. That is, we prove that here the composition conjecture is true, in contrast with the tangential center problem on zero cycles. Finally, we give examples of applications of our results.
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Funding
The first two authors are supported by Ministerio de Economía y Competitividad through the project MTM2017-83568-P (AEI/ERDF, EU) and also partially supported by Junta de Extremadura/FEDER Grant Number IB18023. The first and second authors are also partially supported by Junta de Extremadura/FEDER Grants Numbers GR18001 and GR18023, respectively. The last author was supported by Croatian Science Foundation (HRZZ) grant PZS-2019-02-3055 from Research Cooperability funded by the European Social Fund and by EIPHI Graduate School (contract ANR-17-EURE-0002).
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 3-21 https://doi.org/10.4213/faa3854.
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Álvarez, A., Bravo, J.L., Christopher, C. et al. Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture. Funct Anal Its Appl 55, 257–271 (2021). https://doi.org/10.1134/S0016266321040018
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DOI: https://doi.org/10.1134/S0016266321040018