This is an announcement for the paper “On the numerical index of absolute symmetric norms on the plane” by Javier Merí<https://arxiv.org/search/math?searchtype=author&query=Mer%C3%AD%2C+J>, Alicia Quero<https://arxiv.org/search/math?searchtype=author&query=Quero%2C+A>. Abstract: We give a lower bound for the numerical index of two-dimensional real spaces with absolute and symmetric norm. This allows us to compute the numerical index of the two-dimensional real $L_p$-space for $3/2\leq p\leq 3$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/2002.07529