论文标题
关于具有许多全球K形式的一般类型的投射品种
On projective varieties of general type with many global k-forms
论文作者
论文摘要
我们证明了以下结果：（1）对于任何非字体投影$ 3 $ -folds $ x $的通用类型的$ X $，$χ（\ Mathcal {o} _x）\ neq 2,3 $，规范量$ \ text {vol}（x）$具有最佳的下限$ \ frac $ \ frac {1} $ {420} $; （2）对于非字体投影$ 3 $ -folds（分别$ 4 $ -folds）$ x $的通用类型，带有$ h^{2，0}（x）（x）\ geq 108 \ cdot 42^3+4 $（分别为$ h^{2，0}（x）$ 3 $ 3 $ 3 $ 3 $ - $ 3 $ 5 $ 5- $ 5 $ 5 $ 5 $。 （3）对于任何非字体投影$ n $ -flold $ x $的通用类型的$ q（x）> n \ geq 4 $，规范稳定性指数$ r_s $ r_s（x）$是$（n-1）$ - th Canonical稳定性指数$ r_ r_ r_ {n-1} $的上限。
We prove the following results: (1) for any nonsingular projective $3$-folds $X$ of general type with $χ(\mathcal{O}_X)\neq 2,3$, the canonical volume $\text{Vol}(X)$ has the optimal lower bound $\frac{1}{420}$; (2) for nonsingular projective $3$-folds (resp. $4$-folds) $X$ of general type with $h^{2, 0}(X)\geq 108\cdot 42^3+4$ (resp. with sufficiently large $h^{2, 0}(X)$), the $3$-canonical map (resp. $5$-canonical map) is stably birational; (3) for any nonsingular projective $n$-fold $X$ of general type with $q(X)>n\geq 4$, the canonical stability index $r_s(X)$ is upper bounded by the $(n-1)$-th canonical stability index $r_{n-1}$.
