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cygv

Rust CI Python CI Crates.io Version PyPI - Version PyPI - Downloads

This project implements an efficient algorithm to perform the HKTY procedure [1, 2] to compute Gopakumar-Vafa (GV) and Gromov-Witten (GW) invariants of Calabi-Yau (CY) manifolds obtained as hypersurfaces or complete intersections in toric varieties. This project is based on the work presented in the paper "Computational Mirror Symmetry", but written in the Rust programming language and with some additional improvements.

Command line interface

This project also ships a cygv executable, so that it can be used without Python. It reads YAML-formatted data from a file, or from the standard input, and writes the resulting invariants to a file, or to the standard output.

cargo install cygv
cygv --file input.yaml --output invariants.yaml

It is part of the default cli feature. Library users that do not need it can depend on this crate with default-features = false to avoid pulling in the argument and YAML parsers.

The input is a stream of YAML documents, each of which specifies a single CY manifold.

---
name: an example threefold
generators: [[0, -1], [1, 2]]
grading_vector: [3, -1]
q: [[1, 1, 1, 0, 1, 2], [0, 0, -1, 1, 1, -1]]
intnums:
  - [0, 0, 0, 2]
  - [0, 0, 1, 1]
  - [0, 1, 1, -1]
  - [1, 1, 1, 5]
invariants: gv
min_points: 100

The intersection numbers can equivalently be given as a mapping from indices to values, which is easier to read when there are many of them.

intnums:
  "0,0,0": 2
  "0,0,1": 1
  "0,1,1": -1
  "1,1,1": 5

The results are written back as one YAML document per input document, sorted by the degree of the curve classes under the grading vector.

---
name: an example threefold
invariants: gv
is_threefold: true
grading_vector: [3, -1]
results:
  - {curve_class: [0, -1], degree: 1, gv: -4}
  - {curve_class: [1, 0], degree: 3, gv: 7524}

Run cygv --help for the full list of input fields and options, and see the examples directory for complete inputs.

License

Licensed under the GNU General Public License v3 or later (GPLv3+) (LICENSE or https://www.gnu.org/licenses/gpl-3.0.en.html#license-text).

Contribution

Any contribution submitted for inclusion in the work by you, shall be licensed as under the GPLv3+, without any additional terms or conditions. See CONTRIBUTING.md for guidelines.