Book3264Examples -- Examples using M2 and Schubert2 to do intersection theory

Description

This package consists almost entirely of example code for the main text and exercises of the book '3264 \& All That: Intersection Theory in Algebraic Geometry' by Eisenbud and Harris. Most of the example code relies on the package Schubert2. The information in this package is best accessed via the help or viewHelp commands.

Conventions in effect throughout:

-Blackboard bold is represented in code by doubling a letter, so for example G(2,4) and GG(1,3) are both the Grassmannian of lines in ${\mathbb P}^3$.

Intersection Theory Section 5.2 -- Basics of vector bundles and Chern classes
Intersection Theory Section 5.3 -- Operations on vector bundles
Intersection Theory Section 5.4.1-2 -- Chern class computations on projective space
Intersection Theory Section 5.4.3 -- Tangent bundles to hypersurfaces
Intersection Theory Section 5.4.4 -- Bundles on Grassmannians

Author

Charley Crissman <[email protected]>

Version

This documentation describes version 0.1 of Book3264Examples.

Citation

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

@misc{Book3264ExamplesSource,
  title = {{Book3264Examples: examples to accompany the eponymous book by Eisenbud and Harris. Version~0.1}},
  author = {Charley Crissman},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- diagrams -- Ferrers diagrams contained in a rectangle
- grassmannian (missing documentation)
- placeholderSchubertCycle (missing documentation)
- placeholderToSchubertBasis -- Express cycles on G(k,n) in terms of the Schubert basis
Methods
- diagrams(ZZ,ZZ) -- see diagrams -- Ferrers diagrams contained in a rectangle
- diagrams(ZZ,ZZ,ZZ) -- Partitions contained in a rectangle
- grassmannian(ZZ,ZZ) (missing documentation)
- placeholderSchubertCycle(List,FlagBundle) (missing documentation)
- placeholderToSchubertBasis(RingElement,FlagBundle) -- see placeholderToSchubertBasis -- Express cycles on G(k,n) in terms of the Schubert basis

For the programmer

The object Book3264Examples is a package, defined in Book3264Examples.m2.

The source of this document is in Book3264Examples.m2:186:0.