Seminar in Diophantine Problems

主講者: 郭驥 (本所)
講題: A Complex Analogue of Pisot's $d$-th Root Problem
時間: 2020-03-04 (Wed.)  10:30 - , 13:30 -
地點: 數學所 617 研討室 (台大院區)
Abstract: (I) 10:30 am, (II) 1:30 pm

Let $b(n)$ be a linear recurrence and let $k$ be a number field with $b(n)\in k$ for all $n\in \mathbb N$. Pisot conjectured that if $b(n)$ is a $d$-th power in $k$ for every $n\in\mathbb N$, then there exists a linear recurrence $a(n)$ defined over $\bar k$ such that $b(n)=a(n)^d$ for every $n\in\mathbb N$. We will first discuss a complex analogue of this problem in this talk. Then we will study a special case of the Green-Griffith conjecture for moving targets using a similar method. To be more precise, we will show that a holomorphic map from $\mathbb C$ to $\mathbb P^n$ is algebraically degenerate if it omits a simple normal crossing divisor $D$ which consists of $n-1$ moving hyperplanes and a moving conic.
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