论文标题
有效的特征和川形的质量猜想
Effective Eigendivisors and the Kawaguchi-Silverman Conjecture
论文作者
论文摘要
令$ f \ colon x \ rightarrow x $为在一个数字字段上定义的普通投影品种的过滤内态。 $ f $的动力学可以通过线性动作的动力学$ f^*\ colon pic（x）_ \ mathbb {r} \ rightArrow pic（x）_ \ mathbb {r} $，该动态由$ f^*$的频谱理论控制。令$λ_1（f）$为$ f^*$的光谱半径。我们研究$ \ mathbb {q} $ - 除以$ f^*d =λ_1（f）d $ and $κ（d）= 0 $，其中$κ（d）$是Divisor $ d $的IITAKA维度。我们分析了此类分隔线的基础基因座，并根据Kawaguchi和Silverman描述的约旦街区的规范高度来解释小型特征值集。最后，我们确定了圆形形态上的线性代数条件，这可能在证明川河 - silverman猜想的实例中有用。
Let $f\colon X\rightarrow X$ be a surjective endomorphism of a normal projective variety defined over a number field. The dynamics of $f$ may be studied through the dynamics of the linear action $f^*\colon Pic(X)_\mathbb{R}\rightarrow Pic(X)_\mathbb{R}$, which are governed by the spectral theory of $f^*$. Let $λ_1(f)$ be the spectral radius of $f^*$. We study $\mathbb{Q}$-divisors $D$ with $f^*D=λ_1(f) D$ and $κ(D)=0$ where $κ(D)$ is the Iitaka dimension of the divisor $D$. We analyze the base locus of such divisors and interpret the set of small eigenvalues in terms of the canonical heights of Jordan blocks described by Kawaguchi and Silverman. Finally we identify a linear algebraic condition on surjective morphisms that may be useful in proving instances of the Kawaguchi-Silverman conjecture.
