论文标题
Massey产品和藤田的分解高于更高尺寸的基础
Massey products and Fujita decomposition over higher dimensional base
论文作者
论文摘要
令$ f \ colon x \ y $为尺寸$ n $和$ m $的光滑复杂品种之间的可半纤维。本文包含对De Rham封闭相对一种形式的局部系统和纤维上的顶形式的分析。特别是，后者在更高的尺寸基础上恢复了$ f_*ω__{x/y} $的第二个富士的本地系统。所谓的梅西产品理论允许在自然的卡斯特尔努沃沃斯假说下研究相关的单肌表示的有限性。在这个结果的促进的情况下，我们还确切地确定了Massey产品与Castelnuovo-De typer Type定理之间的密切关系。
Let $f\colon X\to Y$ be a semistable fibration between smooth complex varieties of dimension $n$ and $m$. This paper contains an analysis of the local systems of de Rham closed relative one forms and top forms on the fibers. In particular the latter recovers the local system of the second Fujita decomposition of $f_*ω_{X/Y}$ over higher dimensional base. The so called theory of Massey products allows, under natural Castelnuovo-type hypothesis, to study the finiteness of the associated monodromy representations. Motivated by this result, we also make precise the close relation between Massey products and Castelnuovo-de Franchis type theorems.
