论文标题
较高的du bois和较高的孤立奇异性的理性特性
The higher Du Bois and higher rational properties for isolated singularities
论文作者
论文摘要
最近引入了较高的理性和更高的杜波伊斯奇异点，作为对理性和杜波伊斯奇点的标准定义的自然概括。在本说明中，我们讨论了孤立奇点的这些属性，尤其是在局部完整的交叉点（LCI）情况下。首先，我们谴责一个事实，即$ k $ - 理性的孤立奇异性是$ k $ -du bois，而没有任何LCI假设。对于孤立的LCI奇异性，我们就标准的奇异性不变性方面对$ K $ -DU BOI和$ k $ - 理性的奇异性进行了完整的特征。特别是，我们表明$ k $ -du bois的奇异性是$（k-1）$ - 孤立的LCI奇异性的合理性。在证据的过程中，我们建立了孤立的LCI奇异性不变的人之间的一些新关系，并表明其中许多消失了。这些方法还导致在孤立的LCI情况下快速证明相邻定理的反转。最后，我们讨论了特定于Hypersurface情况的一些结果。
Higher rational and higher Du Bois singularities have recently been introduced as natural generalizations of the standard definitions of rational and Du Bois singularities. In this note, we discuss these properties for isolated singularities, especially in the locally complete intersection (lci) case. First, we reprove the fact that a $k$-rational isolated singularity is $k$-Du Bois without any lci assumption. For isolated lci singularities, we give a complete characterization of the $k$-Du Bois and $k$-rational singularities in terms of standard invariants of singularities. In particular, we show that $k$-Du Bois singularities are $(k-1)$-rational for isolated lci singularities. In the course of the proof, we establish some new relations between invariants of isolated lci singularities and show that many of these vanish. The methods also lead to a quick proof of an inversion of adjunction theorem in the isolated lci case. Finally, we discuss some results specific to the hypersurface case.
