Lyubeznik numbers for nonsingular projective varieties
Lyubeznik numbers for nonsingular projective varieties
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非奇异射影簇的柳别兹尼克数
DOI：
10.1112/blms/bdu089
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发表时间：
2014
影响因子：
0.9
通讯作者：
N. Switala
中科院分区：
文献类型：
--
作者：
N. Switala
本文完全确定了非奇异射影簇V上局部环A在仿射锥顶点处的Lyubeznik数λi，j(A)，其中V定义在特征为零的域上，用V的代数de Rham上同调空间的维度表示.特别地，我们证明了这些数是V的固有数值不变量，尽管它们的定义先验地依赖于嵌入到射影空间。这为特征零点中任意变元的嵌入独立性问题提供了肯定的答案，这个问题仍然是开放的。
In this paper, we determine completely the Lyubeznik numbers λi,j(A) of the local ring A at the vertex of the affine cone over a nonsingular projective variety V , where V is defined over a field of characteristic zero, in terms of the dimensions of the algebraic de Rham cohomology spaces of V . In particular, we prove that these numbers are intrinsic numerical invariants of V , even though a priori their definition depends on an embedding into projective space. This provides supporting evidence for a positive answer to the question of embedding‐independence for arbitrary varieties in characteristic zero, which is still open.