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- catalog abstract "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.".
- catalog contributor b5009129.
- catalog created "c1993.".
- catalog date "1993".
- catalog date "c1993.".
- catalog dateCopyrighted "c1993.".
- catalog description "Includes bibliographical references.".
- catalog description "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.".
- catalog extent "vi, 233 p. :".
- catalog hasFormat "Dynkin graphs and quadrilateral singularities.".
- catalog identifier "0387568778 (New York : acid-free)".
- catalog identifier "3540568778 (Berlin : acid-free) :".
- catalog isFormatOf "Dynkin graphs and quadrilateral singularities.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1548.".
- catalog isPartOf "Lecture notes in mathematics ; 1548".
- catalog issued "1993".
- catalog issued "c1993.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Dynkin graphs and quadrilateral singularities.".
- catalog subject "510 s 516.3/53 20".
- catalog subject "Dynkin diagrams.".
- catalog subject "Geometry, algebraic.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Hypersurfaces.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1548 QA614.58".
- catalog subject "Singularities (Mathematics)".
- catalog title "Dynkin graphs and quadrilateral singularities / Tohsuke Urabe.".
- catalog type "text".