Varieties in Cages: A Little Zoo of Algebraic Geometry

被引：0
作者：
Katz G. [1 ]
机构：
[1] 5 Bridle Path Circle, Framingham, 01701, MA
来源：
Arnold Mathematical Journal | 2022年 / 8卷 / 1期
关键词：
Cages; Cayley–Bacharach theorems; Complete intersections; Hyperplane arrangements; Varieties;
D O I：
10.1007/s40598-021-00189-5
中图分类号：
学科分类号：
摘要：
A d{n}-cageK is the union of n groups of hyperplanes in Pn, each group containing d members. The hyperplanes from the distinct groups are in general position, thus producing dn points where hyperplanes from all groups intersect. These points are called the nodes of K. We study the combinatorics of nodes that impose independent conditions on the varieties X⊂ Pn containing them. We prove that if X, given by homogeneous polynomials of degrees ≤ d, contains the points from such a special set A of nodes, then it contains all the nodes of K. Such a variety X is very special: in particular, X is a complete intersection. © 2021, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
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页码：1 / 17
页数：16
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