论文标题
满足Cayley-Bacharach条件和应用的点的几何形状
Geometry of Points Satisfying Cayley-Bacharach Conditions and Applications
论文作者
论文摘要
在本文中，我们研究了复杂的投影空间中点的几何形状，这些点满足了Cayley-Bacharach条件相对于给定程度的整体曲面的完整线性系统。特别是，我们改善了洛佩兹和皮罗拉的结果，我们表明，如果$ k \ geq 1 $和$γ= \ {p_1，\ dots，p_d \} \ subset \ subset \ mathbb {p}^n $是满足Cayley-Bacharach条件的一组， $ | \ MATHCAL {O} _ {\ MATHBB {p}^n}（k）| $，带有$ d \ leq h（k-h+3）-1 $和$ 3 \ leq h \ leq 5 $，然后$γ$在curve of Leg $ h-1 $中。然后，我们将此结果应用于$ \ mathbb {p}^3 $的平滑表面曲线上的线性系列研究。此外，我们讨论了$ \ mathbb {p}^n $的光滑超曲面以及编成$ 2 $完整的交叉点上的空白。
In this paper, we study the geometry of points in complex projective space that satisfy the Cayley-Bacharach condition with respect to the complete linear system of hypersurfaces of given degree. In particular, we improve a result by Lopez and Pirola and we show that, if $k\geq 1$ and $Γ=\{P_1,\dots,P_d\}\subset \mathbb{P}^n$ is a set of distinct points satisfying the Cayley-Bacharach condition with respect to $|\mathcal{O}_{\mathbb{P}^n}(k)|$, with $d\leq h(k-h+3)-1$ and $3\leq h\leq 5$, then $Γ$ lies on a curve of degree $h-1$. Then we apply this result to the study of linear series on curves on smooth surfaces in $\mathbb{P}^3$. Moreover, we discuss correspondences with null trace on smooth hypersurfaces of $\mathbb{P}^n$ and on codimension $2$ complete intersections.
