论文标题
射击的射击三倍的投影三倍的calabi-yau结构承认两极分化的内态
Log Calabi-Yau structure of projective threefolds admitting polarized endomorphisms
论文作者
论文摘要
让$ x $成为普通的投射品种，承认有两极分化的内态$ f $，即$ f^*h \ sim qh $，用于某些充足的除数$ h $和整数$ q> 1 $。 Broustet和Gongyo猜想$ x $是Calabi-yau类型的，即$（x，δ）$是某些有效的$ \ Mathbb {q} $ - divisor的LC，因此$ k_x+k_x+Δ\ sim _ {\ sim _ {\ shatbb {q}} {\ mathbb {q}}} 0 $。在本文中，我们建立了基于模棱两可的最小模型计划和规范捆绑公式的一般准则。这样，当$ x $是平稳的投影三倍时，我们证明了猜想。
Let $X$ be a normal projective variety admitting a polarized endomorphism $f$, i.e., $f^*H\sim qH$ for some ample divisor $H$ and integer $q>1$. It was conjectured by Broustet and Gongyo that $X$ is of Calabi-Yau type, i.e., $(X,Δ)$ is lc for some effective $\mathbb{Q}$-divisor such that $K_X+Δ\sim_{\mathbb{Q}} 0$. In this paper, we establish a general guideline based on the equivariant minimal model program and the canonical bundle formula. In this way, we prove the conjecture when $X$ is a smooth projective threefold.
