论文标题
最低的非零消失的共同形态功能
Lowest non-zero vanishing cohomology of holomorphic functions
论文作者
论文摘要
我们研究了一个消失的周期复杂的$φ_FA_X$，用于减少的复杂分析空间$ f $ f $ f $ y y -a $ a $ a dedekind域（例如，在$ a $ a $ a $ a $ a的本地化之后，可以将单型eigenvalue分解的整数局部定位。 Assuming the perversity of the shifted constant sheaf $A_X[d_X]$, we show that the lowest possibly-non-zero vanishing cohomology at $0\in X$ can be calculated by the restriction of $φ_fA_X$ to an appropriate nearby curve in the singular locus $Y$ of $f$, which is given by intersecting $Y$ with the intersection of sufficiently general hyperplanes in the环境空间足够在0附近。证明使用Lefschetz型定理，用于本地基本组。在统一的多项式情况下，同样的断言也是Artin的消失定理。通过一个相关的论点，我们可以显示第一个Milnor同子学的非独裁者单构部分的消失，用于许多中央超平面布置，其环境维度至少至少为4。
We study the vanishing cycle complex $φ_fA_X$ for a holomorphic function $f$ on a reduced complex analytic space $X$ with $A$ a Dedekind domain (for instance, a localization of the ring of integers of a cyclotomic field, where the monodromy eigenvalue decomposition may hold after a localization of $A$). Assuming the perversity of the shifted constant sheaf $A_X[d_X]$, we show that the lowest possibly-non-zero vanishing cohomology at $0\in X$ can be calculated by the restriction of $φ_fA_X$ to an appropriate nearby curve in the singular locus $Y$ of $f$, which is given by intersecting $Y$ with the intersection of sufficiently general hyperplanes in the ambient space passing sufficiently near 0. The proof uses a Lefschetz type theorem for local fundamental groups. In the homogeneous polynomial case, a similar assertion follows from Artin's vanishing theorem. By a related argument we can show the vanishing of the non-unipotent monodromy part of the first Milnor cohomology for many central hyperplane arrangements with ambient dimension at least 4.
