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Dynkin Graphs and Quadrilateral Singularities
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Catalogue Information
Field name
Details
Dewey Class
511.5
Title
Dynkin Graphs and Quadrilateral Singularities ([EBook] /) / by Tohsuke Urabe.
Author
Urabe, Tohsuke
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1993.
Physical Details
CCXLVIII, 242 p. : online resource.
Series
Lecture Notes in Mathematics
0075-8434 ; ; 1548
ISBN
9783540477693
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/BFb0084369
Links to Related Works
Subject References:
Algebraic Geometry
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Analysis
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Analysis (Mathematics)
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Graph Theory
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Mathematical analysis
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Mathematics
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Authors:
Urabe, Tohsuke
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Corporate Authors:
SpringerLink (Online service)
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Series:
Lecture Notes in Mathematics
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Classification:
511.5
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