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RESOLUTION GRAPHS AND SPLICE DIAGRAMS

 
Acknowledgements
 
Introduction
 
Resolution Graphs
      Graphs, Vertices and Printing
      Creation from Curve Singularities
      Creation from Pencils
      Creation by Hand
      Modifying Resolution Graphs
      Numerical Data Associated to a Graph
 
Splice Diagrams
      Creation of Splice Diagrams
      Numerical Functions of Splice Diagrams
 
Translation Between Graphs
      Splice Diagrams from Resolution Graphs
 
Bibliography







DETAILS

 
Introduction

 
Resolution Graphs

      Graphs, Vertices and Printing
            g eq h : GrphRes,GrphRes -> BoolElt
            ResolutionGraphVertex(g,i) : GrphRes,RngIntElt -> GrphResVert
            Vertex(v) : GrphResVert -> GrphVert
            ResolutionGraph(v) : GrphResVert -> GrphRes
            IsVertex(g,v) : GrphRes,GrphResVert -> BoolElt
            Index(v) : GrphResVert -> RngIntElt
            v eq w : GrphResVert,GrphResVert -> BoolElt

      Creation from Curve Singularities
            ResolutionGraph(C, p) : Sch, Pt -> GrphRes
            Example GrphRes_singularity (H115E1)

      Creation from Pencils
            ResolutionGraph(P) : LinearSys -> GrphRes
            ResolutionGraph(P,a,b) : LinearSys,RngElt,RngElt -> GrphRes
            Example GrphRes_pencil (H115E2)

      Creation by Hand
            MakeResolutionGraph(g,s,t) : GrphDir,SeqEnum,SeqEnum -> GrphRes
            MakeResolutionGraph(N) : NwtnPgon -> GrphRes
            UnderlyingGraph(g) : GrphRes -> GrphDir

      Modifying Resolution Graphs
            Connect(v,w) : GrphResVert,GrphResVert -> GrphRes
            CalculateCanonicalClass(~g) : GrphRes ->
            Disconnect(v,w) : GrphResVert -> GrphRes
            Component(v) : GrphResVert -> GrphRes
            CalculateMultiplicities(~g) : GrphRes ->
            CalculateTransverseIntersections(~g) : GrphRes ->
            ModifySelfintersection(~v,n) : GrphResVert,RngIntElt ->
            ModifyTransverseIntersection(~v,n) : GrphResVert,RngIntElt ->

      Numerical Data Associated to a Graph
            Size(g) : GrphRes -> RngIntElt
            SelfIntersections(g) : GrphRes -> SeqEnum
            Multiplicities(g) : GrphRes -> SeqEnum
            CanonicalClass(g) : GrphRes -> SeqEnum
            TransverseIntersections(g) : GrphRes -> SeqEnum
            GenusContribution(g) : GrphRes -> RngIntElt
            CartanMatrix(g) : GrphRes -> Mtrx
            Determinant(g) : GrphRes -> RngElt

 
Splice Diagrams

      Creation of Splice Diagrams
            SpliceDiagram(C,p) : Sch,Pt -> GrphSpl
            RegularSpliceDiagram(P) : LinearSys -> GrphSpl
            MakeSpliceDiagram(g,e,a) : GrphDir,SeqEnum,SeqEnum -> GrphSpl
            MakeSpliceDiagram(e,l,a) : SeqEnum,SeqEnum,SeqEnum -> GrphSpl
            SpliceDiagramVertex(s,i) : GrphSpl,RngIntElt -> GrphSplVert
            SpliceDiagram(v) : GrphSplVert -> GrphSpl
            UnderlyingGraph(s) : GrphSpl -> GrphDir
            UnderlyingVertex(v) : GrphSplVert -> GrphVert
            Vertices(s) : GrphSpl -> SeqEnum
            RootVertex(s) : GrphSpl -> GrphSplVert
            Index(v) : GrphSplVert -> RngIntElt
            s eq t : GrphSpl,GrphSpl -> BoolElt

      Numerical Functions of Splice Diagrams
            EdgeLabels(s) : GrphSpl -> SeqEnum
            VertexLabels(s) : GrphSpl -> SeqEnum
            TotalLinking(v) : GrphSplVert -> RngIntElt
            LinkingNumbers(s) : GrphSpl -> SeqEnum
            Linking(u,v) : GrphSplVert,GrphSplVert -> RngIntElt
            EdgeDeterminant(u,v) : GrphSplVert,GrphSplVert -> RngIntElt
            Valency(v) : GrphSplVert -> RngIntElt
            IsRegular(s) : GrphSpl -> BoolElt
            IsReduced(s) : GrphSpl -> BoolElt
            HasIrregularFibres(s) : GrphSpl -> BoolElt
            Degree(s) : GrphSpl -> RngIntElt
            EulerCharacteristic(s) : GrphSpl -> RngIntElt
            Size(s) : GrphRes -> RngIntElt
            Arrows(s) : GrphRes -> SeqEnum
            VertexPath(u,v) : GrphSplVert,GrphSplVert -> SeqEnum,SeqEnum

 
Translation Between Graphs

      Splice Diagrams from Resolution Graphs
            SpliceDiagram(g) : GrphRes -> GrphSpl
            SpliceDiagram(g,v) : GrphRes,GrphResVert -> GrphSpl

 
Bibliography

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013