A Geometric Approach to Some Systems of Exponential Equations
A Geometric Approach to Some Systems of Exponential Equations
复制标题
一些指数方程组的几何方法
DOI：
10.1093/imrn/rnab340
复制
发表时间：
2023
影响因子：
1
通讯作者：
Aslanyan V
中科院分区：
文献类型：
--
作者：
Aslanyan V
Zilber的指数代数闭性猜想(也称为Zilber零点猜想)给出了复代数簇与半交换簇的指数映射图相交的条件。我们证明了猜想的特例，其中簇具有到指数映射域的占优投影，对于交换簇和代数环面。此外，在交集是0维的情况下，我们通过将足够大的点参数化为(多值)解析映射下的周期格的映象来展示交集的结构。我们的方法是复杂几何的，而不是Brownawell和Masser仅针对代数环面给出的真实解析证明。
Zilber’s Exponential Algebraic Closedness conjecture (also known as Zilber’s Nullstellensatz) gives conditions under which a complex algebraic variety should intersect the graph of the exponential map of a semiabelian variety. We prove the special case of the conjecture where the variety has dominant projection to the domain of the exponential map, for abelian varieties and for algebraic tori. Furthermore, in the situation where the intersection is 0-dimensional, we exhibit structure in the intersection by parametrizing the sufficiently large points as the images of the period lattice under a (multivalued) analytic map. Our approach is complex geometric, in contrast to a real analytic proof given by Brownawell and Masser just for the case of algebraic tori.