Advanced Studies in Pure Mathematics

Singular fibers in barking families of degenerations of elliptic curves

Takayuki Okuda

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Singularities in Geometry and Topology 2011, V. Blanlœil and O. Saeki, eds. (Tokyo: Mathematical Society of Japan, 2015), 203-256

Received: 23 May 2012
Revised: 10 December 2013
First available in Project Euclid: 19 October 2018

Permanent link to this document euclid.aspm/1539916288

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D06: Fibrations, degenerations
Secondary: 14H15: Families, moduli (analytic) [See also 30F10, 32G15] 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 32S50: Topological aspects: Lefschetz theorems, topological classification, invariants

Degeneration of complex curves splitting family elliptic curve singular fiber monodromy


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.

Export citation