Estimates of the number of rational mappings from a fixed variety to varieties of general type
Estimates of the number of rational mappings from a fixed variety to varieties of general type
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从固定品种到一般类型品种的理性映射数量估计
DOI：
10.5802/aif.1581
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
G. Dethloff
中科院分区：
文献类型：
--
作者：
T. Bandman;G. Dethloff
首先，我们找到了两个固定光滑射影簇之间的显性有理映射$f：X\right tarrow Y$的个数的有效界。其中$n=dimX$，$K_X$是$X$的典范丛，$A，B$是一些仅依赖于$n$的常量。然后证明了对于任一簇$X$，都存在具有如下性质的数$c(X)$和$C(X)$：对于任意三重的一般类型的$Y$，占优有理映射的个数$f：X\r Y$在上面由$c(X)$有界.存在占优有理映射$f：X\r Y$的模二元等价的三重数$Y$的上界是$C(X)$。此外，如果$X$是三重一般类型，我们证明了$c(X)$和$C(X)$仅依赖于$X$的典范模型$X_c$的指标$r_{X_c}$和$K_{X_c}^3$。
First we find effective bounds for the number of dominant rational maps $f:X \rightarrow Y$ between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type $\{A \cdot K_X^n\}^{\{B \cdot K_X^n\}^2}$, where $n=dimX$, $K_X$ is the canonical bundle of $X$ and $A,B $ are some constants, depending only on $n$. Then we show that for any variety $X$ there exist numbers $c(X)$ and $C(X)$ with the following properties: For any threefold $Y$ of general type the number of dominant rational maps $f:X \r Y$ is bounded above by $c(X)$. The number of threefolds $Y$, modulo birational equivalence, for which there exist dominant rational maps $f:X \r Y$, is bounded above by $C(X)$. If, moreover, $X$ is a threefold of general type, we prove that $c(X)$ and $C(X)$ only depend on the index $r_{X_c}$ of the canonical model $X_c$ of $X$ and on $K_{X_c}^3$.
DOI：
10.1090/s0894-0347-1992-1149195-9
发表时间：
1992-09
影响因子：
3.9
作者：
J. Kollár;S. Mori
通讯作者：
J. Kollár;S. Mori