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.点击此处访问可检索的ldp-database网页界面。 ldp-database存储了容许非平凡代数环面（algebraic torus）作用的复对数德尔佩佐曲面（log del Pezzo surfaces）。该数据库中的条目要么为托里曲面（toric surfaces），要么为带有非平凡环面作用的非托里曲面。用户可通过多种不变量与性质对ldp-database进行检索，包括皮卡数（Picard number）、戈伦斯坦指数（Gorenstein index）、对数典范性（log canonicity）、反典范自交数（anticanonical self intersection）等。 ldp-database收录了满足下述性质且容许环面作用的对数德尔佩佐曲面的完整分类： 皮卡数为1且戈伦斯坦指数不超过200（271203条记录，详见文献[1]）， 1/3对数典范曲面（129904条记录，详见文献[2]）， 皮卡数为1且皮卡指数不超过10000的托里曲面（68053条记录，详见文献[3]）， 皮卡数为1且皮卡指数不超过2500的非托里曲面（106355条记录，详见文献[3]）， 皮卡数不超过2且戈伦斯坦指数不超过200的全固有二次曲面（72081条记录，详见文献[4]）， 皮卡数为3且戈伦斯坦指数不超过40的全固有二次曲面（106591条记录，详见文献[4]）， 总体而言，ldp-database共收录692125个曲面族。该数据库无冗余，即所有不同条目对应的曲面均互不同构。 用户可通过SQLite格式文件ldp.db下载该数据库。schema.txt文件中包含了数据库可用字段的相关说明。可直接通过SQLite工具或CStarSurfaces.jl软件包对该数据库进行查询。此外，还提供了网页界面，用户可通过搜索表单完成数据库检索。