Subordinate fibers of Takamura splitting families for stellar singular fibers

Abstract

Takamura constructed a theory on splitting families of degenerations of Riemann surfaces. We call them Takamura splitting families. In a Takamura splitting family, there appear two kinds of singular fibers, called a main fiber and subordinate fibers. In this paper, when the original singular fiber is stellar and the core is a projective line, we determine the number of subordinate fibers and describe the types of singular points, which are nodes.