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Dynkin Graphs and Quadrilateral Singularities

Tohsuke Urabe (Autor)

Buch | Softcover

CCXLVIII, 242 Seiten

1993 | 1993
Springer Berlin (Verlag)
978-3-540-56877-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	29.7.1993
Reihe/Serie	Lecture Notes in Mathematics
Reihe/Serie	Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn
Zusatzinfo	CCXLVIII, 242 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	380 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	Algebraic Curve • Algebraic Geometry • Deformation • Dynkin Graph • Graph • SiM • singular fiber • Singularity
ISBN-10	3-540-56877-8 / 3540568778
ISBN-13	978-3-540-56877-3 / 9783540568773
Zustand	Neuware