It's no secret I like
- making websites
- classification results
and one classification I found myself going back to over and over again is that of Fano 3-folds. These are smooth projective varieties of dimension 3 such that the anticanonical bundle $\omega_X^\vee$ is ample. These have been classified by Iskovskikh and Mori–Mukai. It turns out there are 105 different families, with interesting relationships between them.
At fanography.info I've created an online tool to study this classification, combining information from quite a few different sources.
There are still some things I would like to add, such as
- more information on the minimal model program: extremaly rays, birational transformations
- semiorthogonal decompositions
- dimensions of the automorphism groups
- information on toric geometry
- information on mirror symmetry
but I guess it's better to just release it as it is, instead of waiting for me to finish this.
If you want to contribute by adding information or adding explanations, please get in touch!