In the paper we present new examples of unexpected varieties. The research on unexpected varieties started with a paper of Cook II, Harbourne, Migliore and Nagel and was continued in the paper of Harbourne, Migliore, Nagel and Teitler. Here we present three ways of producing unexpected varieties that expand on what was previously known. In the paper of Harbourne, Migliore, Nagel and Teitler, cones on varieties of codimension 2 were used to produce unexpected hypersurfaces. Here we show that cones on positive dimensional varieties of codimension 2 or more almost always give unexpected hypersurfaces. For non-cones, almost all previous work has been for unexpected hypersurfaces coming from finite sets of points. Here we construct unexpected surfaces coming from lines in \(\mathbb {P}^3\), and we generalize the construction using birational transformations to obtain unexpected hypersurfaces in higher dimensions.

在本文中，我们提出了意想不到的品种的新例子。对意外品种的研究始于Cook II，Harbourne，Migliore和Nagel的论文，并在Harbourne，Migliore，Nagel和Teitler的论文中继续进行。在这里，我们介绍三种产生意料之外的品种的方法，这些方法会在以前已知的基础上扩展。在Harbourne，Migliore，Nagel和Teitler的论文中，使用余量2的圆锥体产生了意外的超曲面。在这里，我们显示余量为2或更大的正维变体上的圆锥几乎总是会产生意外的超曲面。对于非圆锥体，几乎所有以前的工作都是针对来自有限点集的意外超曲面。在这里，我们构造来自\（\ mathbb {P} ^ 3 \）中的线的意外曲面，并且我们使用birational变换对构造进行了概括，以获得了更高尺寸的意外超曲面。