Anabelian properties of tame fundamental groups of singular curves

Abstract

In anabelian geometry, we consider to what extent the \'{e}tale or tame fundamental groups of schemes reflect geometric properties of the schemes. Although there are many known results (mainly for smooth curves) in this area, general singular curves have rarely been treated. One reason is that we cannot determine the isomorphism classes of singular curves themselves from their \'{e}tale or tame fundamental groups in general. On the other hand, Das proved that the structure of the tame fundamental group of a singular curve over an algebraically closed field is determined by its normalization and an invariant relating to its singularities. In the present paper, by using this and known anabelian results, we determine the isomorphism classes of the normalizations of singular curves over various fields under certain conditions.