论文标题
投影二元性，意外的超曲面和超平面布置的对数推导
Projective Duality, Unexpected Hypersurfaces and Logarithmic Derivations of Hyperplane Arrangements
论文作者
论文摘要
已经写了几篇论文，研究了意外的突出表面。我们说，如果脂肪线性子空间的一般结合较少，则一组有限的积分承认了意外的超曲面。这是一个更强的条件，考虑到一些先前认为出乎意料的突出表面的解释。 然后，我们开发了二元理论，将非常出乎意料的超曲面的研究与双重平面布置的衍生作用相关联。这使我们能够将结果概括为库克，哈伯恩，米格里奥尔，纳格尔·法恩齐和瓦利斯的平面。特别是，我们给出一个标准，以确定Z集是否在Z中是否允许Z中非常出乎意料的突出表面，这是在不可减至的反射组对环境投射空间的作用下不变的。 我们的方法即使在投影平面上也有新的应用程序，在该平面上我们能够在Z点上放置强大的条件，该点Z可以接受某些类型的意外曲线。我们关闭了Terao的Freeness猜想，以将线路排列与猜想相关联，该猜想是G. dirac在真实平面中点的配置上。
Several papers have been written studying unexpected hypersurfaces. We say a finite set of points Z admits unexpected hypersurfaces if a general union of fat linear subspaces imposes less that the expected number of conditions on the ideal of Z. In this paper, we introduce the concept of a very unexpected hypersurface. This is a stronger condition which takes into account an explanation for some hypersurfaces previously considered unexpected. We then develop a duality theory to relate the study of very unexpected hypersurfaces to the derivations of dual hyperplane arrangements. This allows us to generalize results in the plane of Cook, Harbourne, Migliore, Nagel Faenzi, and Vallés to higher dimensions. In particular, we give a criterion to determine if a set Z admits very unexpected hypersurfaces in the case Z is invariant under the action of an irreducible reflection group on the ambient projective space. Our approach has new applications even in the projective plane where we are able to place strong conditions on sets of points Z which admit certain types of unexpected curves. We close relating Terao's Freeness Conjecture for line arrangements to a conjecture due to G. Dirac on configurations of points in the real plane.
