论文标题
关于Artinian本地完整的Condimension的Hilbert功能
On the Hilbert function of Artinian local complete intersections of codimension three
论文作者
论文摘要
在奇异理论或代数几何形状中，很自然地研究特殊代数$ a $的希尔伯特功能，例如局部完整的交叉点或更一般的戈伦斯坦代数。由于Macaulay和Stanley，经过很好的理解，以{}标准分级完整交集的{}希尔伯特函数出现的序列进行了很好的理解。除了编成二次，在当地情况下，几乎没有知名度。在本文中，我们表征了二次Artinian的Hilbert函数，即Codimension三的完整交集。有趣的是，我们证明，当且只有在这样一个完整的交叉点上可以接受时，就可以接受这种戈伦斯坦环的功能。我们为给定的希尔伯特功能提供了有效的局部完整交叉点的结构。我们证明，这种完整的相交理想的对称分解取决于其希尔伯特功能。
In singularity theory or algebraic geometry, it is natural to investigate possible Hilbert functions for special algebras $A$ such as local complete intersections or more generally Gorenstein algebras. The sequences that occur as {the} Hilbert functions of standard graded complete intersections are well understood classically thanks to Macaulay and Stanley. Very little is known in the local case except in codimension two. In this paper we characterise the Hilbert functions of quadratic Artinian complete intersections of codimension three. Interestingly we prove that a Hilbert function is admissible for such a Gorenstein ring if and only if is admissible for such a complete intersection. We provide an effective construction of a local complete intersection for a given Hilbert function. We prove that the symmetric decomposition of such a complete intersection ideal is determined by its Hilbert function.
