Other Applied Mathematics Commons^™

Algorithms To Compute Characteristic Classes, Martin Helmer

Electronic Thesis and Dissertation Repository

In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).

We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …