# Composantes connexes et irréductibles en familles - Mathematics > Algebraic Geometry

Abstract: For an algebraic stack $\sX$ flat and of finite presentation over a scheme$S$, we introduce various notions of {\em relative connected components} and{\em relative irreducible components}. The main distinction between thesenotions is whether we require the total space of a relative component to beopen or closed in $\sX$. We study the representability of the associatedfunctors of relative components, and give an application to the moduli stack ofcurves of genus $g$ admitting an action of a fixed finite group $G$.

Author: Matthieu Romagny IMJ

Source: https://arxiv.org/