论文标题
几何顶点分解和联络
Geometric vertex decomposition and liaison
论文作者
论文摘要
几何顶点分解和联络是两个框架，这些框架用于产生有关代数品种类似的结果。在本文中，我们在这些方法之间建立了明确的联系。特别是，我们表明，每个几何顶点可分解的理想都由一系列具有高度1的基本G-纤维化序列连接到一个不确定的理想，相反，某种类型的每种G-Biliaison都会引起几何角度的顶点分解。因此，我们可以立即得出结论，包括舒适的几个理想家族，包括舒伯特决定性的理想，定义了各种复合物的理想，并定义了分级的下限群集代数的理想。
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.
