几何顶点分解与联络
Geometric vertex decomposition and liaison
AI总结：
本文建立了几何顶点分解与联络两种框架间的显式联系，证明几何顶点可分解理想通过高度为1的初等G-联络与不定元理想相连，并由此推出多个已知理想族为glicci。
摘要：
几何顶点分解与联络是两种框架，已被用于对相似的代数簇族产生相似的结果。在本文中，我们建立了这两种方法之间的显式联系。特别地，我们证明了每个几何顶点可分解理想都通过一系列高度为1的初等G-联络与一个不定元理想相联络，并且反过来，某种类型的每个G-联络都会产生一个几何顶点分解。作为推论，我们可以立即得出结论，几个众所周知的理想族是glicci的，包括舒伯特行列式理想、复形簇的定义理想以及分次下界簇代数簇的定义理想。
英文摘要：
Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this paper, we establish an explicit connection between these approaches. In particular, we show that each geometrically vertex decomposable ideal is linked by a sequence of elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, that every G-biliaison of a certain type gives rise to a geometric vertex decomposition. As a consequence, we can immediately conclude that several well-known families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of graded lower bound cluster algebras.
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