The ToricVarieties_project aims for high performance algorithms to compute sheaf cohomologies of coherent (toric) sheaves.
| Package | Description |
|---|---|
| ToricVarieties | Support for toric varieties in gap. |
| AdditionsForToricVarieties | Additional algorithms for toric varieties (soon to be joined with the toric varieties package) |
| cohomCalgInterface | An interface to cohomcalg |
| TopcomInterface | An interface to topcom |
| SpasmInterface | An interface to spasm |
| SparseMatrices | Elementary support for sparse matrices. This packages uses SpasmInterface |
| TruncationsOfFPGradedModules | We model coherent sheaves a f.p. graded modules via FreydCategories. This package installs truncations for these modules. |
| ToolsForFPGradedModules | This package installs constructors for ideals, minimal free resolutions, Betti tables but also conversion of our f.p. graded modules into other module formats employed throughout the homalg_project. |
| CoherentSheavesOnToricVarieties | This package models coherent sheaves as objects in a Serre quotient category of f.p. graded modules. |
| SheafCohomologyOnToricVarieties | Implementation of fast algorithms for the computation of sheaf cohomologies of coherent (toric) sheaves. The algorithms are described in my PhD thesis. These algorithms have been used in the context of F-theory in the article 1706.04616. |
| H0Approximator | This package is the result of recent collaboration with Mirjam Cvetič, Ron Donagi, Ling Lin, Muyang Liu and Fabian Rühle. The preprint is available here. |
| QSMExporer | This package is the result of recent collaboration with Mirjam Cvetič and Muyang Liu. The preprint is be available on the arxiv 2104.08297. |
Detailed instructions for the installation can be found here. For Ubuntu and Debian systems, I provide an installation script, with attempts to set up all of the above packages. This script is available here.
The work of Martin Bies is supported by SFB-TRR 195 Symbolic Tools in Mathematics and their Application of the German Research Foundation (DFG).