论文标题
仿射空间的条件环
Ring of conditions for affine space
论文作者
论文摘要
指数总和是加法组$ \ mathbb c^n $的字符的线性组合。指数分析集（EAS）是ESS有限元组的一组常见零。我们将ES和EAS视为Laurent多项式的类似物和复杂圆环$（\ Mathbb {C} \ setMinus0）^n $中的代数变体的类似物。我们分别为$ \ mathbb c^n $构造条件环，作为$（\ mathbb {c} \ setMinus0）^n $的条件环类似物。该环的构造基于与某些多维圆环的EAS代数亚变量相关的定义，以及将热带代数几何形状应用于此亚变量。就像在圆环的情况下一样，条件环由Hypersurfaces产生。该预印本是提交给“ Izvestiya：数学”的文章的扩展摘要。
The exponential sum (ES) is a linear combination of characters of an additive group $\mathbb C^n$. The exponential analytic set (EAS) is a set of common zeroes of a finite tuple of ESs. We consider ES and EAS as an analogs of Laurent polynomial and of algebraic variety in complex torus $(\mathbb{C}\setminus0)^n$. Respectively we construct the ring of conditions for $\mathbb C^n$ as an analog of the ring of conditions for $(\mathbb{C}\setminus0)^n$. The construction of this ring is based on the definition of associated to EAS algebraic subvariety of some multidimensional torus and on the applying tropical algebraic geometry to this subvariety. Just as in the case of a torus, the ring of conditions is generated by hypersurfaces. This preprint is an extended summary of the article proposed to "Izvestiya: Mathematics".
