A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties. (English) Zbl 1378.14061
Summary: 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 J. Fullwood [J. Singul. 8, 1–10 (2014; Zbl 1315.14009)] 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 \(\mathbb{P}^n\).
MSC:
| 14Q15 | Computational aspects of higher-dimensional varieties |
| 14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |
| 14-04 | Software, source code, etc. for problems pertaining to algebraic geometry |
| 14M10 | Complete intersections |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
Euler characteristic; computer algebra; computational intersection theory; Chern-Schwartz-MacPherson class; Chern classCitations:
Zbl 1315.14009References:
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