论文标题
新的奇异性不变性：捆$β_x^\子弹$
New singularity invariants : the sheaf $β_X^\bullet$
论文作者
论文摘要
在[b.18]中为任何减少的纯尺寸复合空间$ x $构建的分级相干捆绑$α_x^\ bullet $是外部产品稳定的，而不是由de rham差异。我们在这里构建了一个新的分级连贯的捆$α_x^\ bullet $，其中包含$α_x^\ bullet $和外部产品和de rham差异的稳定。我们证明，它再次具有``撤回属性''，用于holomorphic Maps $ f：x \ to y $之间的``supback topperion''，以至于$ f（x）$在$ y $的单数集中不包含$ f（x）$。此外，这种分级的连贯的捆绑$α_x^\子弹$具有天然相干的详尽过滤，并且这种过滤也与此类全体形态图与背背兼容。这些滑轮在单一复杂空间上定义了新不变的。我们在一些简单的示例中表明，这些不变性是新的。
The graded coherent sheaf $α_X^\bullet$ constructed in [B.18] for any reduced pure dimensional complex space $X$ is stable by exterior product but not by the de Rham differential. We construct here a new graded coherent sheaf $α_X^\bullet$ containing $α_X^\bullet$ and stable both by exterior product and by the de Rham differential. We show that it has again the ``pull-back property'' for holomorphic maps $f : X \to Y$ between irreducible complex spaces such that $f(X)$ is not contained in the singular set of $Y$. Moreover, this graded coherent sheaf $α_X^\bullet$ comes with a natural coherent exhaustive filtration and this filtration is also compatible with the pull-back by such holomorphic maps. These sheaves define new invariants on singular complex spaces. We show on some simple examples that these invariants are new.
