The Hartshorne–Hirschowitz theorem says that a generic union of lines in ${\mathbb{P}}^n$, $(n\ge 3)$, has good postulation. The proof of Hartshorne and Hirschowitz in the initial case ${\mathbb{P}}^3$ is handled by a method of specialization via a smooth quadric surface with the property of having two rulings of skew lines. We provide a proof in the case ${\mathbb{P}}^3$ based on a new degeneration of disjoint lines via a plane $H\cong {\mathbb{P}}^2$, which we call $(2,s)$-cone configuration, that is a schematic union of s intersecting lines passing through a single point P together with the trace of an s-multiple point supported at P on the double plane 2H. In the first part of this paper, we discuss our degeneration inductive approach. We prove that a $(2,s)$-cone configuration is a degeneration of s disjoint lines in ${\mathbb{P}}^3$, or more generally in ${\mathbb{P}}^n$. In the second part of the paper, we use this degeneration in an effective method to show that a generic union of lines in ${\mathbb{P}}^3$ imposes independent conditions on the linear system $|{\mathcal{O}}_{{\mathbb{P}}^3}(d)|$ of surfaces of given degree d. The basic motivation behind our degeneration approach is that it looks more systematic that gives some hope of extensions to the analogous problem in higher dimensional spaces, that is the postulation problem for m-dimensional planes in ${\mathbb{P}}^{2m+1}$.

Hartshorne – Hirschowitz定理说， ${\mathbb{P.}}^{ñ}$， $（ñ\ge \mathrm{第三名}）$，具有很好的假设。Hartshorne和Hirschowitz在初始案例中的证明${\mathbb{P.}}^{\mathrm{第三名}}$通过具有光滑二次曲面的专业化方法处理具有具有两条斜线规则的特性。在这种情况下，我们提供证明${\mathbb{P.}}^{\mathrm{第三名}}$ 基于通过平面的不连续线的新退化 $H\cong {\mathbb{P.}}^{\mathrm{2个}}$，我们称之为 $（\mathrm{2个}，s）$圆锥形结构的确是通过单个点P的s条相交线的示意性结合，以及在双平面2 H上在P处支撑的s个多点的轨迹。在本文的第一部分，我们讨论了退化归纳法。我们证明$（\mathrm{2个}，s）$-圆锥配置是s中不相交线的退化${\mathbb{P.}}^{\mathrm{第三名}}$，或更一般而言 ${\mathbb{P.}}^{ñ}$。在本文的第二部分中，我们将这种退化用于一种有效的方法，以表明${\mathbb{P.}}^{\mathrm{第三名}}$ 对线性系统施加独立条件 $|{\mathcal{Ø}}_{{\mathbb{P.}}^{\mathrm{第三名}}}（d）|$给定度数为d的曲面的数量。我们退化方法背后的基本动机是，它看起来更加系统化，从而为扩展高维空间中的类似问题（即m维平面的假设问题）提供了一些希望。${\mathbb{P.}}^{\mathrm{2个}米+\mathrm{1个}}$。