Dynkin Graphs and Quadrilateral Singularities (Paperback, 1993 ed.)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Mathematisches Institut der Universitat und Max-Planck-Institut fur Mathematik, Bonn, 1548
Release date:	July 1993
First published:	1993
Authors:	Tohsuke Urabe
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Paperback
Pages:	242
Edition:	1993 ed.
ISBN-13:	978-3-540-56877-3
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > General Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN:	3-540-56877-8
Barcode:	9783540568773

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