论文标题
计算Fano问题的Galois组
Computing Galois groups of Fano problems
论文作者
论文摘要
FANO问题包括在多种情况下枚举固定尺寸的线性空间，从而概括了立方表面上27行的经典问题。那些有限的许多线性空间的Fano问题具有相关的Galois组，该组作用于这些线性空间，并控制通过自由基在坐标中计算它们的复杂性。约旦首先研究了Fano问题的Galois组，后者考虑了Galois组在立方表面上的27行。最近，Hashimoto和Kadets在特殊情况下确定了所有其他FANO问题，并表明所有其他FANO问题都使Galois组包含交替组，从而几乎将所有FANO问题归类。我们使用计算工具来证明，中等大小的几个FANO问题的GALOIS组等于对称组，每个组都不知道。
A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of 27 lines on a cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group that acts on these linear spaces and controls the complexity of computing them in coordinates via radicals. Galois groups of Fano problems were first studied by Jordan, who considered the Galois group of the problem of 27 lines on a cubic surface. Recently, Hashimoto and Kadets nearly classified all Galois groups of Fano problems by determining them in a special case and by showing that all other Fano problems have Galois group containing the alternating group. We use computational tools to prove that several Fano problems of moderate size have Galois group equal to the symmetric group, each of which were previously unknown.
