Fano 3-folds

Magma code to recreate all the Hilbert series data of the Fano database.

As well as computing precise plurigenus data, this code makes a first estimate of the degrees of generators of the anticanonical ring. This is done naively, and is only plausible in small codimension. The improvements used for the Fano database are made by comparison with the K3 database and some consideration of the polarisation at each singularity.

The Fano database can be downloaded from

Canonical 3-folds and Calabi-Yau 3-orbifolds

Magma code to generate the databases of canonical and Calabi-Yau 3-folds.

l-Reflexive polygons

Magma code to recreate the classification of l-reflexive polygons.

LDP (log del Pezzo) polygons

Tables of the LDP-polygons of index at most 17.

Terminal Gorenstein weighted projective space

Plain text copies of the classification of terminal Gorenstein weighted projective space in dimensions 5 to 10 (along with the source code used to generate them).

4-dimensional terminal and canonical weighted projective space

Plain text copies of the classification of terminal and canonical weighted projective space in dimension 4 (along with source code). The web page also contains the classification of all 1-point lattice simplices in dimension 4.

Tom and Jerry

A Big Table of results of the Tom and Jerry programme for constructing index 1 Fano 3-folds in codimension 4. The magma code that generates this data (together with instructions on use) is also available.

Quasismooth hypersurfaces

Magma code to calculate classifications of well-formed, quasismooth hypersurfaces in weighted projective space. After unpacking (tar xvfz hsfcode.tar.gz), see the README file for instructions. The resulting fourfold classifications are also available to download.

Sarkisov links in dimension 4

A plain text copy of the web of toric Sarkisov links arising from the 35,947 four-dimensional terminal fake weighted projective spaces. We compute all point blowups of discrepancy at most 5, and simple curve and surface blowups, and for each one either extend to a Sarkisov link or discard as a bad link. Magma source code used for this calculation is also available. See the README for details.