next | previous | forward | backward | up | top | index | toc | packages | Macaulay2 website
EnumerationCurves :: EnumerationCurves

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

Version

This documentation describes version 0.1 of EnumerationCurves.

Source code

The source code from which this documentation is derived is in the file EnumerationCurves.m2.

Exports

  • Functions and commands
  • 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.