## Advanced Studies in Pure Mathematics

### Singular fibers in barking families of degenerations of elliptic curves

Takayuki Okuda

#### Abstract

Takamura [Ta3] established a theory of splitting families of degenerations of complex curves of genus $g \ge 1$. He introduced a powerful method for constructing a splitting family, called a barking family, in which the resulting family of complex curves has a singular fiber over the origin (the main fiber) together with other singular fibers (subordinate fibers). He made a list of barking families for genera up to 5 and determined the main fibers appearing in them. This paper determines most of the subordinate fibers of the barking families in Takamura's list for the case $g = 1$. (There remain four undetermined cases.) Also, we show that some splittings never occur in a splitting family.

#### Article information

Dates
Revised: 10 December 2013
First available in Project Euclid: 19 October 2018

https://projecteuclid.org/ euclid.aspm/1539916288

Digital Object Identifier
doi:10.2969/aspm/06610203

Mathematical Reviews number (MathSciNet)
MR3382051

Zentralblatt MATH identifier
1360.14032

#### Citation

Okuda, Takayuki. Singular fibers in barking families of degenerations of elliptic curves. Singularities in Geometry and Topology 2011, 203--256, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06610203. https://projecteuclid.org/euclid.aspm/1539916288