The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in Pn
The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in Pn
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DOI：
10.1016/j.aim.2021.108035
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发表时间：
2019-10
影响因子：
1.7
通讯作者：
Laurent Busé;A. Dimca;H. Schenck;Gabriel Sticlaru
中科院分区：
文献类型：
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作者：
Laurent Busé;A. Dimca;H. Schenck;Gabriel Sticlaru
对于降阶超曲面，Milnor代数的Castelnuovo-Mumford正则性在何时是光滑的以及何时是孤立奇点是很容易理解的。我们研究了当存在正维奇异轨迹时的正规性。在某些情况下，我们证明了正则性是有界的，它是的黑森多项式的次数。然而，情况并不总是这样，我们证明了在Milnor代数的正则性中可以二次增长。
For a reduced hypersurfaceof degree, the Castelnuovo-Mumford regularity of the Milnor algebrais well understood whenis smooth, as well as whenhas isolated singularities. We study the regularity ofwhenhas a positive dimensional singular locus. In certain situations, we prove that the regularity is bounded by, which is the degree of the Hessian polynomial of. However, this is not always the case, and we prove that inthe regularity of the Milnor algebra can grow quadratically in.