论文标题
对数基础改变定理和对数规范除数积极性的平稳下降
Logarithmic base change theorem and smooth descent of positivity of log canonical divisor
论文作者
论文摘要
我们证明了对数基础的基础定理，用于推动pluri-canonical束的推动，并使用它来推断日志规范除数的阳性特性通过光滑的投射形态下降。作为一个应用程序，对于$κ（x）\ ge 0 $和$ -k_y $ big，对于过滤型形态$ f：x \ to y $，我们证明$ y \ y \ y \ y \setminusΔ（f）$是log enter nog类型，其中$δ（f）$是歧视轨迹。特别是，当$ y = \ mathbb {p}^n $时，我们有$ \dimδ（f）= n-1 $和$ \ m atrm {deg} \，δ（f）\ ge n+2 $，概括了$ n = 1 $ viehweg-zuo证明的情况。此外，我们证明了Popa对平滑代数纤维空间的对数Kodaira维度的超级药物的猜想在最多三个尺寸的基础上，并分析相关问题。
We prove a logarithmic base change theorem for pushforwards of pluri-canonical bundles and use it to deduce that positivity properties of log canonical divisors descend via smooth projective morphisms. As an application, for a surjective morphism $f:X\to Y$ with $κ(X)\ge 0$ and $-K_Y$ big, we prove $Y\setminus Δ(f)$ is of log general type, where $Δ(f)$ is the discriminant locus. In particular, when $Y=\mathbb{P}^n$ we have $\dim Δ(f)=n-1$ and $\mathrm{deg}\,Δ(f)\ge n+2$, generalizing the case $n=1$ proved by Viehweg-Zuo. In addition, we prove Popa's conjecture on the superadditivity of the logarithmic Kodaira dimension of smooth algebraic fiber spaces over bases of dimension at most three and analyze related problems.
