Local monodromy on the fundamental groups of algebraic curves along a degenerate stable curve Original Research Article

We consider the universal local deformation of a stable pointed curve and the associated monodromy representation on the fundamental group of a smooth fiber of this deformation. The image of the monodromy is an abelian subgroup of the outer automorphism of the fundamental group of a smooth fiber, and has a filtration induced from the weight filtration of the fundamental group. By using a graph of groups, we give a combinatorial description of the monodromy representation, and show that the induced filtration is determined by graph-theoretic invariants of the dual graph of the stable pointed curve.