Vol. 7, No. 1, 2015

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Computing characteristic classes and the topological Euler characteristic of complex projective schemes

Christine Jost

Vol. 7 (2015), 31–39

The Macaulay2 package CharacteristicClasses provides commands for the computation of the topological Euler characteristic, the degrees of the Chern classes and the degrees of the Segre classes of a closed subscheme of complex projective space. The computations can be done both symbolically and numerically, the latter using an interface to Bertini. We provide some background for the implementation, show how to use the package with the help of examples and compare its performance to other implementations.

Chern classes, Segre classes, topological Euler characteristic, computational algebraic geometry
Mathematical Subject Classification 2010
Primary: 14C17
Secondary: 14Q15, 65H10
Supplementary material

CharacteristicClasses version 1.1

Received: 11 July 2014
Accepted: 5 June 2015
Published: 14 July 2015
Christine Jost
Ericsson Research
Färögatan 6
SE-164 80 Stockholm