This is an announcement for the paper "Geometry of the $L_q$-centroid bodies of an isotropic log-concave measure" by Apostolos Giannopoulos, Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou. Abstract: We study some geometric properties of the $L_q$-centroid bodies $Z_q(\mu )$ of an isotropic log-concave measure $\mu $ on ${\mathbb R}^n$. For any $2\ls q\ls\sqrt{n}$ and for $\varepsilon \in (\varepsilon_0(q,n),1)$ we determine the inradius of a random $(1-\varepsilon )n$-dimensional projection of $Z_q(\mu )$ up to a constant depending polynomially on $\varepsilon $. Using this fact we obtain estimates for the covering numbers $N(\sqrt{\smash[b]{q}}B_2^n,tZ_q(\mu ))$, $t\gr 1$, thus showing that $Z_q(\mu )$ is a $\beta $-regular convex body. As a consequence, we also get an upper bound for $M(Z_q(\mu ))$. Archive classification: math.FA math.MG Submitted from: apgiannop@math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.0246 or http://arXiv.org/abs/1306.0246