Splice diagrams arise from resolution graphs by a reduction procedure and conversely resolution graphs arise from splice diagrams by a continued fraction calculation. At present, Magma only incorporates the former calculation. However, when a splice diagram s has been constructed using a curve singularity, the corresponding resolution graph g is calculated and can be recovered using the function CorrespondingResolutionGraph. The vertices of s correspond to a subset of those of g. The correspondence can be recovered with the function CorrespondingVertices.
By default Magma always makes the reduced splice diagram since otherwise many determinants would be calculated unnecessarily.
The translation of resolution graph g to splice diagram is done in two steps. First the underlying graph of g is reduced by the removal of all vertices of valency 2 (including arrows in the valency calculation). Then the edge labels are calculated using determinants of subgraphs.
L: RngIntElt Default: 0
K: RngIntElt Default: 0
Reduced: RngIntElt Default: 1
A splice diagram of the resolution graph g. All parameters can take the value 0 or 1. If Reduced is 1 then the splice diagram will be reduced, otherwise it will be the splice diagram on the underlying graph of g.The parameter L refers to the total linking numbers of the vertices of the resulting splice diagram. The parameter K refers to the canonical class of the vertices of the resulting splice diagram. Each quantity will be calculated when the corresponding parameter is 1.
The splice diagram of the resolution graph g with the condition that the vertex v will not be removed by a reduction.