The functionality outlined below, and much more, is implemented in Hodge diamond cutter, which can be used in Sage. If you use it for your research, please cite it using DOI.

Recall that a few months ago I wrote a tool to visualise / compute Serre duality and Hodge diamonds for complete intersections.

Using it yesterday I realised that I should beef it up a little, so I have:

  • added more numerical invariants in the case of surfaces, they are defined in terms of the Hodge diamond anyway but it saves me from miscomputing things (I should do it for more general varieties too, but at the moment I care only about surfaces)
  • improved the layout, no more incessant scrolling if you care about Hodge diamonds

The result still won't win a medal for its visuals. If you have suggestions regarding layout or functionality, just contact me.