论文标题
v滤光度和最小指数，用于本地完整的交叉点奇点
V-filtrations and minimal exponents for locally complete intersection singularities
论文作者
论文摘要
我们定义并研究了平滑复合体代数$ x $的本地交叉点的亚cheme $ z $的最小指数概念，从而扩展了Saito在Hypersurfaces的情况下定义的不变性。我们的定义是根据与$ z $相关的kashiwara-malgrange $ v $滤光。我们表明，最小指数描述了Hodge过滤和订单过滤在本地共同体$ H^r_z（{\ Mathcal O} _x）$上一致，其中$ r $是$ z $ in $ x $中的$ z $。我们还研究了它与$ z $的伯恩斯坦 - 撒托多项式的关系。我们的主要结果描述了与合适的超表面相关的不变式的较高的编码亚气管的最小指数；这允许通过将Codimension $ 1 $案例减少来证明此不变的主要属性。 A key ingredient for our main result is a description of the Kashiwara-Malgrange $V$-filtration associated to any ideal $(f_1,\ldots,f_r)$ in terms of the microlocal $V$-filtration associated to the hypersurface defined by $\sum_{i=1}^rf_iy_i$.
We define and study a notion of minimal exponent for a locally complete intersection subscheme $Z$ of a smooth complex algebraic variety $X$, extending the invariant defined by Saito in the case of hypersurfaces. Our definition is in terms of the Kashiwara-Malgrange $V$-filtration associated to $Z$. We show that the minimal exponent describes how far the Hodge filtration and order filtration agree on the local cohomology $H^r_Z({\mathcal O}_X)$, where $r$ is the codimension of $Z$ in $X$. We also study its relation to the Bernstein-Sato polynomial of $Z$. Our main result describes the minimal exponent of a higher codimension subscheme in terms of the invariant associated to a suitable hypersurface; this allows proving the main properties of this invariant by reduction to the codimension $1$ case. A key ingredient for our main result is a description of the Kashiwara-Malgrange $V$-filtration associated to any ideal $(f_1,\ldots,f_r)$ in terms of the microlocal $V$-filtration associated to the hypersurface defined by $\sum_{i=1}^rf_iy_i$.
