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Except for this paragraph, and a change in title, this
is a copy of my 'professional' website as it stood when I finished in
academia. My EPSRC postdoctoral fellowship at Oxford finished in
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This page contains a few things that I hope may be useful.
I have attempted to gather together all known pairs of Hodge numbers (h11, h21) of three-dimensional Calabi–Yau manifolds, and sorted them in two ways. In the first list, they are sorted first by h11, then h11+h21, and in the second list they are sorted first by h11+h21 and then by h11. The lists and associated references can be downloaded in this single zip file, or separately: list 1, list 2, references. I would like to acknowledge that I am building on the efforts of Philip Candelas, who collected together the majority of the existing data several years ago.
If you notice that I am missing any examples, please send me an email and I will add them. I have tried to provide at least one reference for each distinct manifold, but have not necessarily referenced all independent discoveries of particular manifolds.
Previously, I had apologised here that the data was only available as plain text, rather than a proper database. This is no longer true, thanks to the efforts of Benjamin Jurke. His Calabi–Yau 3-fold Explorer allows you to search the list of known manifolds, and easily create pretty coloured plots, among other things.
By far the largest class of known Calabi–Yau threefolds are the hypersurfaces in toric fourfolds, constructed by Max Kreuzer and Harald Skarke. The data for these manifolds are also available in a separate database here.
These notes are informal, and typically do not contain references. Although they all written by me, I do not claim that any of the material is original. They represent my understanding of the subjects, sometimes come to on my own, sometimes gained primarily from a single source, and sometimes drawn together from many sources.