Name: dynkin graphs and quadrilateral singularities
SKU: 3485698
Price: 52.37 EUR
Availability: InStock
Author: urabe
ISBN: 9783540568773

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portada dynkin graphs and quadrilateral singularities

dynkin graphs and quadrilateral singularities

Type

Physical Book

Publisher

Springer

Author

urabe

Language

English

Pages

233

ISBN

3540568778

ISBN13

9783540568773

Synopsis "dynkin graphs and quadrilateral singularities"

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.