论文标题
关于高表向与一般还原曲线的交叉点的希尔伯特功能
On the Hilbert function of intersections of a hypersurface with general reducible curves
论文作者
论文摘要
令$ w \ subset \ mathbb {p}^n $，$ n \ ge 3 $，为$ k $ hypersurface。考虑一个“通用”可简化但连接的，曲线$ y \ subset \ mathbb {p}^n $，例如，与$ p_a（y）= 0 $的线条结合了足够的通用连接和节点结合，即一条线。我们研究了$ y \ cap w $的Hilbert功能，其基数$ k°（y）$，并证明是预期的。我们将$ k = 2 $的例外分类和$ n = k = 3 $进行分类。我们将这些结果和工具应用于$ y $是平滑曲线的情况下，使用$ \ Mathcal {o} _y（1）$ nonteptial。
Let $W\subset \mathbb {P}^n$, $n\ge 3$, be a degree $k$ hypersurface. Consider a "general" reducible, but connected, curve $Y\subset \mathbb {P}^n$, for instance a sufficiently general connected and nodal union of lines with $p_a(Y)=0$, i.e. a tree of lines. We study the Hilbert function of the set $Y\cap W$ with cardinality $k°(Y)$ and prove when it is the expected one. We give complete classification of the exceptions for $k=2$ and for $n=k=3$. We apply these results and tools to the case in which $Y$ is a smooth curve with $\mathcal {O}_Y(1)$ non-special.
