Author | Urabe, Tohsuke. author |
---|---|

Title | Dynkin Graphs and Quadrilateral Singularities [electronic resource] / by Tohsuke Urabe |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1993 |

Connect to | http://dx.doi.org/10.1007/BFb0084369 |

Descript | CCXLVIII, 242 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Algebraic geometry
Mathematical analysis
Analysis (Mathematics)
Graph theory
Mathematics
Graph Theory
Algebraic Geometry
Analysis