A polynomial generalization of the Euler characteristic for algebraic sets

Miguel A. Marco-Buzunáriz, with an appendix by J. V. Rennemo

Journal of Singularities
volume 4 (2012), 114-130

Received: 10 January 2012. Received in revised form: 13 April 2012.

DOI: 10.5427/jsing.2012.4g

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Abstract:

We present a method to compute the Euler characteristic of an algebraic subset of C^n. This method relies on classical tools such as Gröbner basis and primary decomposition. The existence of this method allows us to define a new invariant for such varieties. This invariant is related to the problem of counting rational points over finite fields. In an appendix, Jørgen Vold Rennemo proves the relation between this invariant and the Chern-Schwartz-MacPherson class of the variety.

Author(s) information:

Miguel A. Marco-Buzunáriz

email: mmarco@unizar.es