skip to content
Dynkin graphs and quadrilateral singularities Preview this item
ClosePreview this item
Checking...

Dynkin graphs and quadrilateral singularities

Author: Tohsuke Urabe
Publisher: Berlin ; New York : Springer-Verlag, ©1993.
Series: Lecture notes in mathematics (Springer-Verlag), 1548.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Urabe, Tohsuke, 1953-
Dynkin graphs and quadrilateral singularities.
Berlin ; New York : Springer-Verlag, ©1993
(DLC) 93002182
(OCoLC)28222350
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tohsuke Urabe
ISBN: 9783540477693 3540477691
OCLC Number: 289052002
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (vi, 233 pages) : illustrations.
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: 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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1548.
Responsibility: Tohsuke Urabe.
More information:

Abstract:

Along with an exposition of Dynkin graphs and quadrilateral singularities, this monograph demonstrates how the study of hypersurface quadrilateral singularities can be reduced to the study of  Read more...

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/289052002> # Dynkin graphs and quadrilateral singularities
    a schema:MediaObject, schema:CreativeWork, schema:Book ;
    library:oclcnum "289052002" ;
    library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/30595812#Place/berlin> ; # Berlin
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/gw> ;
    schema:about <http://dewey.info/class/510/e20/> ;
    schema:about <http://id.worldcat.org/fast/965830> ; # Hypersurfaces
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/dynkin_graph> ; # Dynkin-Graph
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/algebraische_meetkunde> ; # Algebraïsche meetkunde
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/flache> ; # Fläche
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/singularites_mathematiques> ; # Singularités (Mathématiques)
    schema:about <http://id.worldcat.org/fast/900334> ; # Dynkin diagrams
    schema:about <http://id.worldcat.org/fast/1119502> ; # Singularities (Mathematics)
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/singularitat_mathematik> ; # Singularität (Mathematik)
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/dynkin_diagrammes_de> ; # Dynkin, Diagrammes de
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/hyperflache> ; # Hyperfläche
    schema:bookFormat schema:EBook ;
    schema:copyrightYear "1993" ;
    schema:creator <http://viaf.org/viaf/17310256> ; # Tohsuke Urabe
    schema:datePublished "1993" ;
    schema: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."@en ;
    schema:description "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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/30595812> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://worldcat.org/issn/0075-8434> ; # Lecture notes in mathematics,
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/30595812#Series/lecture_notes_in_mathematics_springer_verlag> ; # Lecture notes in mathematics (Springer-Verlag) ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/28222350> ;
    schema:name "Dynkin graphs and quadrilateral singularities"@en ;
    schema:productID "289052002" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/289052002#PublicationEvent/berlin_new_york_springer_verlag_1993> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/30595812#Agent/springer_verlag> ; # Springer-Verlag
    schema:url <http://www.springerlink.com/openurl.asp?genre=issue&issn=0075-8434&volume=1548> ;
    schema:url <http://dx.doi.org/10.1007/BFb0084369> ;
    schema:url <http://catalog.hathitrust.org/api/volumes/oclc/28222350.html> ;
    schema:workExample <http://worldcat.org/isbn/9783540477693> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/289052002> ;
    .


Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
    schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/30595812#Agent/springer_verlag> # Springer-Verlag
    a bgn:Agent ;
    schema:name "Springer-Verlag" ;
    .

<http://experiment.worldcat.org/entity/work/data/30595812#Series/lecture_notes_in_mathematics_springer_verlag> # Lecture notes in mathematics (Springer-Verlag) ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/289052002> ; # Dynkin graphs and quadrilateral singularities
    schema:name "Lecture notes in mathematics (Springer-Verlag) ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/30595812#Topic/algebraische_meetkunde> # Algebraïsche meetkunde
    a schema:Intangible ;
    schema:name "Algebraïsche meetkunde"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/30595812#Topic/dynkin_diagrammes_de> # Dynkin, Diagrammes de
    a schema:Intangible ;
    schema:name "Dynkin, Diagrammes de"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/30595812#Topic/singularitat_mathematik> # Singularität (Mathematik)
    a schema:Intangible ;
    schema:name "Singularität (Mathematik)"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/30595812#Topic/singularites_mathematiques> # Singularités (Mathématiques)
    a schema:Intangible ;
    schema:name "Singularités (Mathématiques)"@fr ;
    .

<http://id.worldcat.org/fast/1119502> # Singularities (Mathematics)
    a schema:Intangible ;
    schema:name "Singularities (Mathematics)"@en ;
    .

<http://id.worldcat.org/fast/900334> # Dynkin diagrams
    a schema:Intangible ;
    schema:name "Dynkin diagrams"@en ;
    .

<http://id.worldcat.org/fast/965830> # Hypersurfaces
    a schema:Intangible ;
    schema:name "Hypersurfaces"@en ;
    .

<http://viaf.org/viaf/17310256> # Tohsuke Urabe
    a schema:Person ;
    schema:birthDate "1953" ;
    schema:familyName "Urabe" ;
    schema:givenName "Tohsuke" ;
    schema:name "Tohsuke Urabe" ;
    .

<http://worldcat.org/isbn/9783540477693>
    a schema:ProductModel ;
    schema:isbn "3540477691" ;
    schema:isbn "9783540477693" ;
    .

<http://worldcat.org/issn/0075-8434> # Lecture notes in mathematics,
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/289052002> ; # Dynkin graphs and quadrilateral singularities
    schema:issn "0075-8434" ;
    schema:name "Lecture notes in mathematics," ;
    .

<http://www.worldcat.org/oclc/28222350>
    a schema:CreativeWork ;
    rdfs:label "Dynkin graphs and quadrilateral singularities." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/289052002> ; # Dynkin graphs and quadrilateral singularities
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.