chern.lib: a library for symbolic computations with Chern classes

Overview

This library is a toolbox for symbolic computations with Chern classes. The Aluffi's algorithms for computation of characteristic classes of algebraic varieties (Segre, Fulton, Chern-Schwartz-MacPherson classes) are implemented as well (cf. doi:10.1016/S0747-7171(02)00089-5).
The current version of the library chern.lib is available here.
An informal discussion of the algorithms implemented in the library: ps-file , pdf-file .


On different approaches to compute the Chern classes of a tensor product of two vector bundles

A comparison of different algorithms implemented in the library to compute the Chern classes of a tensor product of two vector bundles: ps-file , pdf-file .
Times needed to obtain all the formulas for the Chern classes of tensor products E⊗F with rank(E⊗F)=N.
The Singular code used for testing the four different implementations.



Some examples

The total Chern class and the Hilbert polynomial of the Horrocks-Mumford bundle (cf. doi:10.1016/0040-9383(73)90022-0).

Things that can be computed with the help of the library in around 1 second.
(Laptop 2 x Intel Celeron 2957U @ 1.4 GHz with 8.3 GB of RAM)

The first 38 terms of the Chern character.
The first 16 terms of the Todd class.
The first 12 Chern classes of a tensor product of two bundles.
The Chern classes of all exterior powers of a rank 11 vector bundle of a 3-fold.
The Chern classes of 9 first symmetric powers of a rank 5 vector bundle of a 4-fold.