论文标题
代数纤维空间的数值kodaira尺寸
Numerical Kodaira dimension of algebraic fiber spaces in positive characteristic
论文作者
论文摘要
在本文中，当通用纤维具有NEF规范分裂时，我们证明了Nakayama对代数纤维空间的数值Kodaira维度的积极特征类似物。为此，我们建立了Popa和Schnell的全球一代定理的变体，Viehweg的弱阳性定理和Fujino的全球一代定理具有积极特征。作为副产品，我们表明，当基本空间是一般类型，并且总空间的规范除法相对半样本时，Iitaka的猜想在积极特征中是正确的。
In this paper, we prove a positive characteristic analog of Nakayama's inequality on the numerical Kodaira dimension of algebraic fiber spaces when the generic fibers have nef canonical divisors. To this end, we establish variants of Popa and Schnell's global generation theorem, Viehweg's weak positivity theorem and Fujino's global generation theorem in positive characteristic. As a byproduct, we show that Iitaka's conjecture holds true in positive characteristic when the base space is of general type and the canonical divisor of the total space is relatively semi-ample.
