Dynkin Graphs and Quadrilateral Singularities. (= Lecture Notes in Mathematics, 1548).

Urabe, Tohsuke:

ISBN 10: 3540568778 / ISBN 13: 9783540568773

Editore: Berlin etc.: Springer-Verlag, 1993

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VI, 233 pages with ill.; 24 cm. Good. Former library copy with usual markings. Apart from that inside clean. Cover slightly used. Sprache: Englisch Gewicht in Gramm: 399. Codice articolo 17853

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Titolo: Dynkin Graphs and Quadrilateral ...

Casa editrice: Berlin etc.: Springer-Verlag

Data di pubblicazione: 1993

Legatura: Softcover/Paperback.

Condizione: Gut

Descrizione articolo

Riassunto:

The study of hypersurface quadrilateral singularities can bereduced to the study of elliptic K3 surfaces with a singularfiber of type I * 0 (superscript *, subscript 0), andtherefore these notes consider, besides the topics of thetitle, such K3 surfaces too.The combinations of rational double points that can occur onfibers in the semi-universal deformations of quadrilateralsingularities are examined, to show that the possiblecombinations can be described by a certain law from theviewpoint of Dynkin graphs. This is equivalent to sayingthat the possible combinations of singular fibers inelliptic K3 surfaces with a singular fiber of type I * 0(superscript *, subscript 0) can be described by a certainlaw using classical Dynkin graphs appearing in the theoryof semi-simple Lie groups. Further, a similar descriptionfor thecombination of singularities on plane sextic curvesis given. Standard knowledge of algebraic geometry at thelevel of graduate students is expected. A new method basedon graphs will attract attention of researches.

Contenuti:

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.