论文标题
椭圆形的calabi-yau品种的界限与合理部分
Boundedness of elliptic Calabi-Yau varieties with a rational section
论文作者
论文摘要
我们表明，对于每个固定尺寸$ d \ geq 2 $，$ d $ d $二维的KLT KLT椭圆品种具有数值微不足道的规范捆绑包，只要在代码符号中构成同构，前提是规范类别的扭转索引，并且椭圆形纤维纤维构成了一个有限的部分。这种情况基于与有界扭转索引的一组合理连接的log-yau对的类似界限结果。在尺寸$ 3 $中，我们证明了更一般性的声明，即$ε$ -lc对$（x，b）$（x，b）$ at $ - （k_x +b）$ nef和合理连接的$ x $的组合至编码象征中的同构。
We show that for each fixed dimension $d\geq 2$, the set of $d$-dimensional klt elliptic varieties with numerically trivial canonical bundle is bounded up to isomorphism in codimension one, provided that the torsion index of the canonical class is bounded and the elliptic fibration admits a rational section. This case builds on an analogous boundedness result for the set of rationally connected log Calabi-Yau pairs with bounded torsion index. In dimension $3$, we prove the more general statement that the set of $ε$-lc pairs $(X,B)$ with $-(K_X +B)$ nef and rationally connected $X$ is bounded up to isomorphism in codimension one.
