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001 978-3-540-47769-3
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007 cr nn 008mamaa
008 121227s1993 gw | s |||| 0|eng d
020 _a9783540477693
_9978-3-540-47769-3
024 7 _a10.1007/BFb0084369
_2doi
050 4 _aQA166-166.247
072 7 _aPBV
_2bicssc
072 7 _aMAT013000
_2bisacsh
072 7 _aPBV
_2thema
082 0 4 _a511.5
_223
100 1 _aUrabe, Tohsuke.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDynkin Graphs and Quadrilateral Singularities
_h[electronic resource] /
_cby Tohsuke Urabe.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1993.
300 _aCCXLVIII, 242 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ;
_v1548
505 0 _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.
520 _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.
650 0 _aGeometry, algebraic.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aGraph Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M29020
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662212240
776 0 8 _iPrinted edition:
_z9783540568773
830 0 _aMathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ;
_v1548
856 4 0 _uhttps://doi.org/10.1007/BFb0084369
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9773
_d9773