Institute of Mathematics for Industry

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Splitting singular fibers for degenerations of complex curves


Hold Date 2011-06-17 16:00~2011-06-17 17:00

Place Lecture Room S-1, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Takayuki OKUDA (Kyushu University)

summary:
A degeneration of complex curves is a proper surjective holomorphic map
from a complex surface to a unit disk with a singular fiber over the
origin which is a fibration of complex curves out of the origin.
S. Takamura (Kyoto Univ.) introduced "barking deformations" --- a method
to obtain a deformation family of degenerations by perturbing the
equations locally determining the complex surface in a complex 3-mfd ---
and classified "atomic fibers", that is, unsplittable singular fibers,
by deforming given singular fibers into more simple ones.
What types of singular fibers appear under such deformations? I have
showed most cases for degenerations of elliptic curves. In this talk, I
will present this result with some examples, after I give a short
introduction to Takamura's theory.