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 $\mathbb{P}^n$.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.4113
- arXiv:
- arXiv:1410.4113
- Bibcode:
- 2014arXiv1410.4113H
- Keywords:
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- Mathematics - Algebraic Geometry;
- Computer Science - Symbolic Computation;
- 14Qxx;
- 68W30;
- 14C17;
- 13P15;
- 65H10;
- F.2.2;
- I.1.2;
- I.1.1
- E-Print:
- 47 pages, 3 tables, with Appendix by Martin Helmer and Eric Schost