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Dynkin Graphs and Quadrilateral Singularities : Lecture Notes in Mathematics - Tohsuke Urabe

Dynkin Graphs and Quadrilateral Singularities

Lecture Notes in Mathematics

Paperback Published: 29th July 1993
ISBN: 9783540568773
Number Of Pages: 242

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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.

Quadrilateral singularities and elliptic K3 surfaces.- Theorems with the Ik-conditions for J 3,0, Z 1,0 and Q 2,0.- Obstruction components.- Concept of co-root modules.

ISBN: 9783540568773
ISBN-10: 3540568778
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 242
Published: 29th July 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.32
Weight (kg): 0.35