Log del Pezzo surfaces with torus action - a searchable database

Click here for a searchable web interface for the ldp-database

The ldp-database stores complex log del Pezzo surfaces admitting a non-trivial action by an algebraic torus. So the entries are either toric surfaces or non-toric with a non-trivial-action. The ldp-database is searchable through various invariants and properties such as Picard number, Gorenstein index, log canonicity, anticanonical self intersection and more.

The ldp-database contains complete classifications of log del Pezzo surfaces admitting a torus action with the following properties:

• Picard number 1 and Gorenstein index at most 200 (271.203 entries, see [1]),
• 1/3-log canonical, (129.904 entries, see [2]),
• toric of Picard number 1 and Picard index at most 10.000 (68.053 entries, see [3]),
• non-toric of Picard number 1 and Picard index at most 2500 (106.355 entries, see [3]),
• full intrinsic quadrics of Picard number at most 2 and Gorenstein index at most 200 (72.081 entries, see [4]),
• full intrinsic quadrics of Picard number 3 and Gorenstein index at most 40 (106.591 entries, see [4]),

In total, the ldp-database contains 692.125 families of surfaces. The ldp-database is redundancy free, that means that different entries are non-isomorphic.

The ldp-database can be downloaded in the form of the SQLite file ldp.db. The file schema.txt contains information about the available columns. The database can be queried directly through sqlite or via the software package CStarSurfaces.jl. Additionally, there is a web interface where the database can be queried through a search form.