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Dynkin Graphs and Quadrilateral Singularities
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Dynkin Graphs and Quadrilateral Singularities (Paperback)

£40.99
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Synopsis

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.

Science & MathematicsMathematicsGeometryAlgebraic geometryScience & MathematicsMathematicsMathematical foundations Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Publication Date: 29/07/1993 ISBN-13: 9783540568773  Details: Type: Paperback Format: Books
Availability: Printed to order. Despatched in 2-3 weeks.  

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