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 ${\mathbb P}^3$.

Author

Charley Crissman <[email protected]>

Version

This documentation describes version 0.1 of Book3264Examples.

Source code

The source code from which this documentation is derived is in the file Book3264Examples.m2.

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
- "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.

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