A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties

Abstract

Let $V$ be a possibly singular scheme-theoretic complete intersection subscheme of ${\mathbb{P}}^n$ over an algebraically closed field of characteristic zero. Using a recent result of Fullwood ("On Milnor classes via invariants of singular subschemes", Journal of Singularities) we develop an algorithm to compute the Chern-Schwartz-MacPherson class and Euler characteristic of $V$. This algorithm complements existing algorithms by providing performance improvements in the computation of the Chern-Schwartz-MacPherson class and Euler characteristic for certain types of complete intersection subschemes of ${\mathbb{P}}^n$.

47 pages, 3 tables, with Appendix by Martin Helmer and Eric Schost

References in corpus (2)

• D-brane Deconstructions in IIB Orientifolds
• An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties

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• On CSM classes via Chern-Fulton classes of f-schemes