Singular fibers in barking families of degenerations of elliptic curves

TL;DR

This paper classifies subordinate fibers in barking families of degenerations of elliptic curves, expanding understanding of singular fibers in complex curve degenerations.

Contribution

It determines the types of subordinate fibers in barking families specifically for degenerations of elliptic curves, a new classification in this context.

Findings

Classification of subordinate fibers in elliptic curve degenerations

Extension of Takamura's barking family theory

Detailed types of subordinate fibers identified

Abstract

Takamura established a theory on splitting families of degenerations of complex curves. He introduced a powerful method for constructing a splitting family, called a barking family, in which there appear not only a singular fiber over the origin but also singular fibers over other points, called subordinate fibers. In this paper, for the case of degenerations of elliptic curves, we determine the types of these subordinate fibers.