HodgeIntegrals is a package for evaluating intersection numbers on the Deligne-Mumford moduli space of n-pointed stable curves of genus g, often denoted M_{g,n}. This package evaluates integrals of the form
where the values of ψ_{i}, k_{i}, and λ_{i} are defined as follows:
A good introduction to M_{g,n} and related spaces can be found in the textbook [HM]. Two good references for the algebraic classes ψ_{i}, k_{i}, and λ_{i}, as well as their properties, are [AC] and [M].
This package is modelled after Carel Faber's Maple program KaLaPs, available for download [F]. For more details on how this package works, please read [Y].
[AC] Arbarello, E. and Cornalba, M. Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves. J. Algebraic Geom. 5. (1996), no. 4, 705--749.
[F] Faber, Carel. Maple program for calculating intersection numbers on moduli spaces of curves. Available at http://math.stanford.edu/~vakil/programs/index.html.
[HM] Harris J., and Morrison, I. Moduli of Curves, Graduate Texts in Mathematics 187. Springer-Verlag, New York, 1996. ISBN: 0387984291.
[V] Vakil, R. The moduli space of curves and Gromov-Witten theory. Enumerative invariants in algebraic geometry and string theory (Behrend and Manetti eds.), Lecture Notes in Mathematics 1947, Springer, Berlin, 2008.
[Y] Yang, S., Intersection numbers on M_{g,n}.
The following person has generously contributed code or worked on our code.
Version 1.2.1 of this package was accepted for publication in volume 2 of the journal The Journal of Software for Algebra and Geometry: Macaulay2 on 2010-04-17, in the article Intersection numbers on Mbar_{g,n}. That version can be obtained from the journal or from the Macaulay2 source code repository, svn://svn.macaulay2.com/Macaulay2/trunk/M2/Macaulay2/packages/HodgeIntegrals.m2, release number 11250.
This documentation describes version 1.2.1 of HodgeIntegrals.
The source code from which this documentation is derived is in the file HodgeIntegrals.m2.