论文标题
关于莫里梦境中的Hypersurfaces的Nef和可移动锥的评论
Remarks on nef and movable cones of hypersurfaces in Mori dream spaces
论文作者
论文摘要
我们研究了莫里梦境中的高空曲面的Nef和可移动锥。第一个结果是：让$ z $是一个平稳的莫里梦想空间，至少四个，其极端收缩是相对尺寸的纤维类型至少两个，而让$ x $是$ z $的平滑分裂，那么$ x $也是莫里梦想的空间。 第二个结果是：让$ z $是尺寸的fano多种，至少四个，其极端收缩是纤维类型的，让$ x $是一种平稳的反典型的抗典型的超浮射，$ z $，这是一种平稳的calabi-yau-yau-yyau品种，然后是$ x $ $ x $ $ x $的独特最小型号。理性的多面体锥体是对$ x $的有效移动锥的作用的基本领域。 第三个结果是：让$ p：= \ mathbb {p}^n \ times \ cdots \ times \ times \ times \ mathbb {p}^n $ as $ n $ - fold-fold fold fold the $ n $ dipermensional投射空间。令$ x $是$ n+1 $多智能$（1，\ dots，1）$的一般完整交叉点与$ \ dim x \ geq 3 $。然后，$ x $只有许多最小的模型才能达到同构，此外，可移动锥体的群体以$ x $为单位。
We investigate nef and movable cones of hypersurfaces in Mori dream spaces. The first result is: Let $Z$ be a smooth Mori dream space of dimension at least four whose extremal contractions are of fiber type of relative dimension at least two and let $X$ be a smooth ample divisor in $Z$, then $X$ is a Mori dream space as well. The second result is: Let $Z$ be a Fano manifold of dimension at least four whose extremal contractions are of fiber type and let $X$ be a smooth anti-canonical hypersurface in $Z$, which is a smooth Calabi--Yau variety, then the unique minimal model of $X$ up to isomorphism is $X$ itself, and moreover, the movable cone conjecture holds for $X$, namely, there exists a rational polyhedral cone which is a fundamental domain for the action of birational automorphisms on the effective movable cone of $X$. The third result is: Let $P:= \mathbb{P}^n \times \cdots \times \mathbb{P}^n$ be the $N$-fold self-product of the $n$-dimensional projective space. Let $X$ be a general complete intersection of $n+1$ hypersurfaces of multidegree $(1, \dots, 1)$ in $P$ with $\dim X \geq 3$. Then $X$ has only finitely many minimal models up to isomorphism, and moreover, the movable cone conjecture holds for $X$.
