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We study the analogue of the classical infinitesimal center problem in theplane, but for zero cycles. We define the displacement function in this contextand prove that it is identically zero if and only if the deformation has acomposition factor. That is, we prove that here the composition conjecture istrue, in contrast with the tangential center problem on zero cycles. Finally,we give examples of applications of our results.

Infinitesimal Center Problem on zero cycles and the composition conjecture