论文标题
指数总和方程和热带几何形状
Exponential Sums Equations and Tropical Geometry
论文作者
论文摘要
我们展示了Zilber的指数代数封闭性猜想的一个案例，确定该猜想是为品种而成的，这些品种是添加组$ \ Mathbb {C}^n $的线性子空间的产物，并且是多个组$（\ Mathbbbbbbbb {C}}^n $）的代数子（c}^n $）^n $。这相当于求解某些指数总和方程的系统，并且概括了Zilber的旧结果，Zilber需要对多样性的更强有力的假设，例如在实数上定义的线性空间。证明使用变形虫和热带几何学理论。
We show a case of Zilber's Exponential-Algebraic Closedness Conjecture, establishing that the conjecture holds for varieties which split as the product of a linear subspace of the additive group $\mathbb{C}^n$ and an algebraic subvariety of the multiplicative group $(\mathbb{C}^\times)^n$. This amounts to solving certain systems of exponential sums equations, and it generalizes old results of Zilber, which required stronger assumptions on the variety such as the linear space being defined over the real numbers. The proofs use the theory of amoebas and tropical geometry.
