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024 7 $a10.1007/BFb0084369
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035   $a(DE-He213)978-3-540-47769-3
035   $a(MiAaPQ)EBC5586087
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100   $a20220209d1993      uy             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aDynkin graphs and quadrilateral singularities /$fTohsuke Urabe
205   $a1st ed. 1993.
210  1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1993]
210  4$d©1993
215   $a1 online resource (CCXLVIII, 242 p.)
225 0 $aLecture Notes in Mathematics ;$vVolume 1548
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-387-56877-8 
311   $a3-540-56877-8 
327   $aQuadrilateral 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.
330   $aThe study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs will attract attention of researches.
410  0$aMathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ;$v1548
606   $aSingularities (Mathematics)
606   $aHypersurfaces
615  0$aSingularities (Mathematics)
615  0$aHypersurfaces.
676   $a516.35
700   $aUrabe$b Tohsuke$f1953-2011,$060105
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466601703316
996   $aDynkin graphs and quadrilateral singularities$978691
997   $aUNISA