03078nam 2200613 450 99646660170331620220209114943.03-540-47769-110.1007/BFb0084369(CKB)1000000000437147(SSID)ssj0000322778(PQKBManifestationID)12072441(PQKBTitleCode)TC0000322778(PQKBWorkID)10296136(PQKB)10164143(DE-He213)978-3-540-47769-3(MiAaPQ)EBC5586087(Au-PeEL)EBL5586087(OCoLC)1066196856(MiAaPQ)EBC6867846(Au-PeEL)EBL6867846(PPN)155188941(EXLCZ)99100000000043714720220209d1993 uy 0engurnn#008mamaatxtccrDynkin graphs and quadrilateral singularities /Tohsuke Urabe1st ed. 1993.Berlin ;Heidelberg :Springer-Verlag,[1993]©19931 online resource (CCXLVIII, 242 p.)Lecture Notes in Mathematics ;Volume 1548Bibliographic Level Mode of Issuance: Monograph0-387-56877-8 3-540-56877-8 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.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.Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ;1548Singularities (Mathematics)HypersurfacesSingularities (Mathematics)Hypersurfaces.516.35Urabe Tohsuke1953-2011,60105MiAaPQMiAaPQMiAaPQBOOK996466601703316Dynkin graphs and quadrilateral singularities78691UNISA