Background
Urabe, Tohsuke was born on August 3, 1953 in Tokyo, Japan. Son of Syun-ichi and Mariko University.
(The study of hypersurface quadrilateral singularities can...)
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs will attract attention of researches.
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mathematics professor researcher
Urabe, Tohsuke was born on August 3, 1953 in Tokyo, Japan. Son of Syun-ichi and Mariko University.
Bachelor, Kyoto University, Japan, 1978. Master of Arts, Kyoto University, Japan, 1980. Doctor of Philosophy in Mathematics, Kyoto University, Japan, 1984.
Science worker Max-Planck Institute for Mathematics Bonn, Germany, 1987-1989, 98-99. Associate professor mathematics Tokyo Metropolitan University, 1981-1987, 89-98. Professor mathematics Ibaraki (Japan) University, since 1999.
(The study of hypersurface quadrilateral singularities can...)
Married Yasuko Ichikawa, May 25, 1986. 1 child, Mika.