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# EnumerationCurves -- Enumeration of rational curves via torus actions

## Description

EnumerationCurves is a package to compute the physical numbers of rational curves on Calabi-Yau threefolds via torus actions.

The implementation uses the formulas given in the paper of Kontsevich "Enumeration of rational curves via torus actions".

The main idea is to apply the localization theorem of Atiyah and Bott to reduce the computation to integrations over graphs.

## Author

- Hiep Dang <hiepdt_tt@dlu.edu.vn>

## Version

This documentation describes version 0.1 of EnumerationCurves, released December 10, 2013.

## Citation

If you have used this package in your research, please cite it as follows:

    @misc{EnumerationCurvesSource,
      title = {{EnumerationCurves: Enumeration of rational curves via torus actions. Version~0.1}},
      author = {Hiep Dang},
      howpublished = {A \emph{Macaulay2} package available at
        \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
    }

## Exports

- Functions and commands
  - linesHypersurface -- Lines on hypersurfaces
  - multipleCover -- Multiple coverings of rational curves on Calabi-Yau threefolds
  - rationalCurve -- Rational curves on Calabi-Yau threefolds
- Methods
  - `linesHypersurface(ZZ)` -- see linesHypersurface -- Lines on hypersurfaces
  - `multipleCover(ZZ)` -- see multipleCover -- Multiple coverings of rational curves on Calabi-Yau threefolds
  - `rationalCurve(ZZ)` -- see rationalCurve -- Rational curves on Calabi-Yau threefolds
  - `rationalCurve(ZZ,List)` -- see rationalCurve -- Rational curves on Calabi-Yau threefolds

## For the programmer

The object EnumerationCurves is a package, defined in EnumerationCurves.m2.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/EnumerationCurves.m2:895:0.