Gale变换的Projective Geometry
The Projective Geometry of the Gale Transform
摘要：
盖尔变换是射影空间中点集的对合，它以多种形式出现在各种学科中，如最优化、编码理论、θ函数，以及最近在我们证明某些一般点集不能满足最小自由分解猜想中。本文用现代代数几何的观点重新审视Gale变换。我们给出了一个更一般的定义，在有限（局部）Gorenstein子计划的背景下。我们在现代形式的一些更显着的例子发现在过去，我们添加新的建设和连接到其他领域的代数几何。我们推广了编码理论中的Goppa定理，并给出了Castelnuovo理论的新应用。我们提供参考古典和现代的来源。
英文摘要：
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points fail to satisfy the minimal free resolution conjecture. In this paper we reexamine the Gale transform in the light of modern algebraic geometry. We give a more general definition, in the context of finite (locally) Gorenstein subschemes. We put in modern form a number of the more remarkable examples discovered in the past, and we add new constructions and connections to other areas of algebraic geometry. We generalize Goppa's theorem in coding theory and we give new applications to Castelnuovo theory. We give references to classical and modern sources.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
