论文标题
关于从准加权超曲面生长的最小品种
On minimal varieties growing from quasismooth weighted hypersurfaces
论文作者
论文摘要
本文涉及用小规范量的最小品种的构建。 The first part devotes to establishing an effective nefness criterion for the canonical divisor of a weighted blow-up over a weighted hypersurface, from which we construct plenty of new minimal $3$-folds including $59$ families of minimal $3$-folds of general type, several infinite series of minimal $3$-folds of Kodaira dimension $2$, $2$ families of minimal Noether线上的$ 3 $ - 折叠类型，$ 12 $的最低段$ 3 $ fold $ 3 $ folds的通用类型在Noether线附近。在第二部分中，我们证明了具有最小$ n $ n $ folds通用类型的规范量的有效下限，并带有规范尺寸$ n-1 $或$ n-2 $。提供了示例，以表明理论下限在尺寸小于或等于$ 5 $的尺寸上是最佳的，并且在较高的维度上几乎是最佳的。
This paper concerns the construction of minimal varieties with small canonical volumes. The first part devotes to establishing an effective nefness criterion for the canonical divisor of a weighted blow-up over a weighted hypersurface, from which we construct plenty of new minimal $3$-folds including $59$ families of minimal $3$-folds of general type, several infinite series of minimal $3$-folds of Kodaira dimension $2$, $2$ families of minimal $3$-folds of general type on the Noether line, and $12$ families of minimal $3$-folds of general type near the Noether line. In the second part, we prove effective lower bounds of canonical volumes of minimal $n$-folds of general type with canonical dimension $n-1$ or $n-2$. Examples are provided to show that the theoretical lower bounds are optimal in dimension less than or equal to $5$ and nearly optimal in higher dimensions.
