Dynkin Graphs and Quadrilateral Singularities. 1st ed. 1993

種類:

電子ブック

責任表示:

by Tohsuke Urabe

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993

著者名:

• Urabe, Tohsuke.
• SpringerLink (Online service)

シリーズ名:

Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ; 1548

ISBN:

9783540477693 [3540477691]    

注記:

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.
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 wil

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