This is an announcement for the paper "The modified complex Busemann-Petty problem on sections of convex bodies" by Marisa Zymonopoulou. Abstract: Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions. Archive classification: math.FA The source file(s), MCBP.tex: 44421 bytes, is(are) stored in gzipped form as 0807.0776.gz with size 12kb. The corresponding postcript file has gzipped size 104kb. Submitted from: marisa@math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.0776 or http://arXiv.org/abs/0807.0776 or by email in unzipped form by transmitting an empty message with subject line uget 0807.0776 or in gzipped form by using subject line get 0807.0776 to: math@arXiv.org.