论文标题
完整十字路口的多层规律性
Multigraded regularity of complete intersections
论文作者
论文摘要
$ v $是多注明空间中的完整交叉点方案，如果可以由理想的$ i $定义，并与$ \ textrm {codim}（v）$定义。我们研究了$ \ mathbb {p}^n \ times \ mathbb {p}^m $中的完整交叉点方案的多条规律性。我们明确计算了Hilbert函数的许多值$ 0 $二维完整交集。我们表明，这些值仅取决于$ n，m $和$ i $的发电机的双层。结果，我们为$ 0 $二维的完整交叉点提供了急剧的上限。
$V$ is a complete intersection scheme in a multiprojective space if it can be defined by an ideal $I$ with as many generators as $\textrm{codim}(V)$. We investigate the multigraded regularity of complete intersections scheme in $\mathbb{P}^n\times \mathbb{P}^m$. We explicitly compute many values of the Hilbert functions of $0$-dimensional complete intersections. We show that these values only depend upon $n,m$, and the bidegrees of the generators of $I$. As a result, we provide a sharp upper bound for the multigraded regularity of $0$-dimensional complete intersections.
