A POLYNOMIAL GENERALIZATION OF THE EULER CHARACTERISTIC FOR ALGEBRAIC SETS
A POLYNOMIAL GENERALIZATION OF THE EULER CHARACTERISTIC FOR ALGEBRAIC SETS
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DOI：
10.5427/jsing.2012.4g
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发表时间：
2012-01-01
影响因子：
0.4
通讯作者：
Rennemo, J. V.
中科院分区：
文献类型：
--
作者：
Marco-Buzunariz, Miguel A.;Rennemo, J. V.
给出了一种计算C-n代数子集的欧拉特征线的方法。该方法依赖于经典的工具，如Grobner基和初等分解。这种方法的存在使我们能够定义一个新的不变量，这样的品种。这个不变量与有限域上有理点的计数问题有关。在附录中，约根·沃尔德·伦尼莫证明了这个不变量和簇的陈-施瓦茨-麦克弗森类之间的关系。
We present a method to compute the Euler characteristic of an algebraic subset of C-n. This method relies on classical tools such as Grobner 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, Jorgen Vold Rennemo proves the relation between this invariant and the Chern-Schwartz-MacPherson class of the variety.