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VOL. 66 | 2015 Singular fibers in barking families of degenerations of elliptic curves


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.


Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1360.14032
MathSciNet: MR3382051

Digital Object Identifier: 10.2969/aspm/06610203

Primary: 14D06
Secondary: 14D05, 14H15, 32S50

Rights: Copyright © 2015 Mathematical Society of Japan


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