论文标题
有限的Abelian亚组，在男生和双形的自我图中
Finite abelian subgroups in the groups of birational and bimeromorphic selfmaps
论文作者
论文摘要
令$ x $为复杂的投影品种。假设$ x $的二态自动形态包含有限的子组同构为$（\ mathbb {z}/n \ mathbb {z}）^r $ for $ r $固定和$ n $ toction univation univation。我们表明$ r $不超过$ 2 \ dim（x）$。此外，当且仅当$ x $对阿贝里安品种具有宗旨时，平等才能保持。我们还表明，在一些其他假设下，紧凑型Kähler空间的双形型自动形态的类似结果成立。
Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not exceed $2\dim(X)$. Moreover, the equality holds if and only if $X$ is birational to an abelian variety. We also show that an analogous result holds for groups of bimeromorphic automorphisms of compact Kähler spaces, under some additional assumptions.
