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:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

The study of hypersurface quadrilateral singularities can bereduced to the study of elliptic K3 surfaces with a singularfiber of type I * 0 (superscript *, subscript 0), andtherefore these  Read more...

Rating:

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

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

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

Details

Additional Physical Format: Online version:
Urabe, Tohsuke, 1953-
Dynkin graphs and quadrilateral singularities.
Berlin ; New York : Springer-Verlag, ©1993
(OCoLC)624478214
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Tohsuke Urabe
ISBN: 3540568778 9783540568773 0387568778 9780387568775
OCLC Number: 28222350
Description: vi, 233 pages : illustrations ; 24 cm.
Contents: 1. Summary --
2. Quadrilateral singularities and elliptic K3 surfaces --
3. Theory of lattices --
4. Analysis of the lattice P --
5. Root modules --
6. Elementary transformations and tie transformations --
7. The Hasse symbol and the Hilbert symbol --
8. The Coxeter-Vinberg graph --
9. Theorems with the Ik-conditions for J[subscript 3,0], Z[subscript 1,0] and Q[subscript 2,0] --
10. A transcendental isotropic cycle --
11. A transcendental cycle with a positive self-intersection number --
12. Nikulin's lattice theory --
13. Combinations of graphs of type A --
14. The exceptions in Theorem 0.3 --
15. Obstruction components --
16. Theorems with the Ik-conditions for W[subscript 1,0] --
17. Two singular fibers of type I* in the case W[subscript 1,0] --
18. A singular fiber of type II*, III*, IV* in the case W[subscript 1,0] --
19. Combinations of graphs of type A in the case W[subscript 1,0] --
20. The basic graphs for S[subscript 1,0] --
21. The second reduction for S[subscript 1,0] 1 --
22. The second reduction for S[subscript 1,0] 2 --
23. The second reduction for S[subscript 1,0] 3 --
24. The second reduction for S[subscript 1,0] 4 --
25. Two singular fibers of type I* in the case S[subscript 1,0] --
26. A singular fiber of type II*, III*, IV* in the case S[subscript 1,0] --
27. Combinations of graphs of type A in the case S[subscript 1,0] --
28. Concept of co-root modules --
29. Theorems with the Ik-conditions for U[subscript 1,0] --
30. Elliptic K3 surfaces with 3 sections --
31. Graphs with a component of type D, the case of U[subscript 1,0] --
32. Graphs with a component of type E, the case of U[subscript 1,0] --
33. Combinations of graphs of type A in the case U[subscript 1,0] --
34. The exceptions in the case U[subscript 1,0] --
Appendix: Singularities of type A, D, E on plane sextic curves.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1548.
Responsibility: Tohsuke Urabe.
More information:

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/28222350> # Dynkin graphs and quadrilateral singularities
    a schema:Book, schema:CreativeWork ;
    library:oclcnum "28222350" ;
    library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/gw> ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/30595812#Place/berlin> ; # Berlin
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/hypersurfaces> ; # Hypersurfaces
    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://experiment.worldcat.org/entity/work/data/30595812#Topic/dynkin_graph> ; # Dynkin-Graph
    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/algebraische_meetkunde> ; # Algebraïsche meetkunde
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/dynkin_diagrams> ; # Dynkin diagrams
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/hyperflache> ; # Hyperfläche
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/singularities_mathematics> ; # Singularities (Mathematics)
    schema:about <http://experiment.worldcat.org/entity/work/data/30595812#Topic/dynkin_diagrammes_de> ; # Dynkin, Diagrammes de
    schema:about <http://dewey.info/class/510/e20/> ;
    schema:bookFormat bgn:PrintBook ;
    schema:copyrightYear "1993" ;
    schema:creator <http://viaf.org/viaf/17310256> ; # Tohsuke Urabe
    schema:datePublished "1993" ;
    schema:description "1. Summary -- 2. Quadrilateral singularities and elliptic K3 surfaces -- 3. Theory of lattices -- 4. Analysis of the lattice P -- 5. Root modules -- 6. Elementary transformations and tie transformations -- 7. The Hasse symbol and the Hilbert symbol -- 8. The Coxeter-Vinberg graph -- 9. Theorems with the Ik-conditions for J[subscript 3,0], Z[subscript 1,0] and Q[subscript 2,0] -- 10. A transcendental isotropic cycle -- 11. A transcendental cycle with a positive self-intersection number -- 12. Nikulin's lattice theory -- 13. Combinations of graphs of type A -- 14. The exceptions in Theorem 0.3 -- 15. Obstruction components -- 16. Theorems with the Ik-conditions for W[subscript 1,0] -- 17. Two singular fibers of type I* in the case W[subscript 1,0] -- 18. A singular fiber of type II*, III*, IV* in the case W[subscript 1,0] -- 19. Combinations of graphs of type A in the case W[subscript 1,0] -- 20. The basic graphs for S[subscript 1,0] -- 21. The second reduction for S[subscript 1,0] 1 -- 22. The second reduction for S[subscript 1,0] 2 -- 23. The second reduction for S[subscript 1,0] 3 -- 24. The second reduction for S[subscript 1,0] 4 -- 25. Two singular fibers of type I* in the case S[subscript 1,0] -- 26. A singular fiber of type II*, III*, IV* in the case S[subscript 1,0] -- 27. Combinations of graphs of type A in the case S[subscript 1,0] -- 28. Concept of co-root modules -- 29. Theorems with the Ik-conditions for U[subscript 1,0] -- 30. Elliptic K3 surfaces with 3 sections -- 31. Graphs with a component of type D, the case of U[subscript 1,0] -- 32. Graphs with a component of type E, the case of U[subscript 1,0] -- 33. Combinations of graphs of type A in the case U[subscript 1,0] -- 34. The exceptions in the case U[subscript 1,0] -- Appendix: Singularities of type A, D, E on plane sextic curves."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/30595812> ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/30595812#Series/lecture_notes_in_mathematics> ; # 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/624478214> ;
    schema:name "Dynkin graphs and quadrilateral singularities"@en ;
    schema:productID "28222350" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/28222350#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.gbv.de/dms/hbz/toc/ht004951867.pdf> ;
    schema:workExample <http://worldcat.org/isbn/9780387568775> ;
    schema:workExample <http://worldcat.org/isbn/9783540568773> ;
    umbel:isLike <http://d-nb.info/931100526> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/28222350> ;
    .


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> # Lecture notes in mathematics ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/28222350> ; # Dynkin graphs and quadrilateral singularities
    schema:name "Lecture notes in mathematics ;" ;
    .

<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/28222350> ; # 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://experiment.worldcat.org/entity/work/data/30595812#Topic/singularities_mathematics> # Singularities (Mathematics)
    a schema:Intangible ;
    schema:name "Singularities (Mathematics)"@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/9780387568775>
    a schema:ProductModel ;
    schema:isbn "0387568778" ;
    schema:isbn "9780387568775" ;
    .

<http://worldcat.org/isbn/9783540568773>
    a schema:ProductModel ;
    schema:isbn "3540568778" ;
    schema:isbn "9783540568773" ;
    .

<http://www.worldcat.org/oclc/624478214>
    a schema:CreativeWork ;
    rdfs:label "Dynkin graphs and quadrilateral singularities." ;
    schema:description "Online version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/28222350> ; # 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.