The closed cone of a rational series is rational polyhedral

被引：2
|
作者：
Kimura, Shunichi [1 ]
Kuroda, Shigeru [2 ]
Takahashi, Nobuyoshi [1 ]
机构：
[1] Hiroshima Univ, Dept Math, Grad Sch Sci, Higashihiroshima 7398526, Japan
[2] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Hachioji, Tokyo 1920397, Japan
来源：
JOURNAL OF ALGEBRA | 2014年 / 405卷
关键词：
Rationality; Power series; Euler-Chow series;
D O I：
10.1016/j.jalgebra.2014.02.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a multivariate power series f, let Cone(f) denote the cone generated by the exponents of the monomials with nonzero coefficients. Assume that f is an expansion of a rational function p/q with gcd(p, q) = 1. Then we prove that the closure (Cone) over bar (f) is equal to Cone(p) + Cone(q). As applications, we show the irrationality of Euler Chow series of certain algebraic varieties. (C) 2014 Elsevier Inc. All rights reserved.
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页码：243 / 258
页数：16
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