Resolution Graphs and Splice Diagrams (New) [HB 74]

These decorated graphs encode data generated by the resolution machinery. At present they are only attached to resolutions of plane curve singularities, but in due course they may be extended to resolutions of linear systems, surface singularities, etc. The package includes a resolution function for curves adapted to present its output in resolution graph format.

• Creation of resolution graphs and their vertices, either implicitly using resolution routines or Newton Polygons, or explicitly by listing the required data
• Calculation of numerical data associated to blowups, e.g., the canonical class of certain rational surfaces
• The Cartan matrix of a graph and associated calculations such as the contribution to the genus of a plane curve of a singularity having a given graph as its resolution
• Surgery on resolution graphs such as cutting an edge of a graph
• Creation of splice diagrams implicitly and explicitly
• Edge determinants and linking numbers of splice diagrams
• Test for regularity of splice diagrams
• Translation between resolution graphs and splice diagrams