一般可约曲线超曲面交点的Hilbert函数

E. Ballico
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引用次数: 0

摘要

让 $W\subset \mathbb {P}^n$, $n\ge 3$是一个学位 $k$ 超曲面。考虑一条“一般的”可约但相连的曲线 $Y\subset \mathbb {P}^n$,例如,具有的线的足够一般的连接和节点并 $p_a(Y)=0$,即一行的树。我们研究了集合的希尔伯特函数 $Y\cap W$ 具有基数性 $k°(Y)$ 并证明它是预期的。我们对例外情况进行了完整的分类 $k=2$ 对于 $n=k=3$. 我们将这些结果和工具应用于 $Y$ 曲线是光滑的吗 $\mathcal {O}_Y(1)$ 非特殊的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Hilbert Function of Intersections of a Hypersurface with General Reducible Curves
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.
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