论文标题
Fujita分解和梅西的纤维品种产品
Fujita decomposition and Massey product for fibered varieties
论文作者
论文摘要
令$ f \ colon x \ to b $为一个可半固定的纤维化，其中$ x $是平滑的尺寸$ n \ geq 2 $和$ b $的平滑曲线。我们为相对$ 1 $形式的本地系统和相对顶级形式提供了结构定理。这给出了$ f_*ω__{x/b} $的第二个富吉塔分解的整洁解释。我们应用解释以表明较高的非理性铅笔的存在，归根结底，以及在自然Castelnuovo型假设上对局部子系统的自然单肌表示的有限性。最后，如果$ b = \ mathbb {p}^1 $，我们给出一个标准，即$ x $不是Albanese通用类型。
Let $f\colon X\to B$ be a semistable fibration where $X$ is a smooth variety of dimension $n\geq 2$ and $B$ is a smooth curve. We give the structure theorem for the local system of the relative $1$-forms and of the relative top forms. This gives a neat interpretation of the second Fujita decomposition of $f_*ω_{X/B}$. We apply our interpretation to show the existence, up to base change, of higher irrational pencils and on the finiteness of the associated monodromy representations under natural Castelnuovo-type hypothesis on local subsystems. Finally we give a criterion to have that $X$ is not of Albanese general type if $B=\mathbb{P}^1$.
