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摘要翻译：
本文研究了Groebner基理论的主要工具之一，即对先导项理想的平面变形，推广到边界基设置的问题。在证明了基于变形到理想程度的简单方法只能在附加假设下工作后，我们引入了边界基格式和泛边界基族。在它们的帮助下，问题可以被改写为在边界基格式上寻找某种有理曲线。我们用不同的方法构造了边界基格式的消失理想生成元系统，并研究了如何使其极小化的问题。对于齐次理想，我们还引入了齐次边界基格式，并证明了它在某些情况下是仿射空间。在这些情况下，很容易明确地写下所需的变形。
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英文标题：
《Deformations of Border Bases》
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作者：
Martin Kreuzer, Lorenzo Robbiano
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the deformation to the degree form ideal works only under additional hypotheses, we introduce border basis schemes and universal border basis families. With their help the problem can be rephrased as the search for a certain rational curve on a border basis scheme. We construct the system of generators of the vanishing ideal of the border basis scheme in different ways and study the question of how to minimalize it. For homogeneous ideals, we also introduce a homogeneous border basis scheme and prove that it is an affine space in certain cases. In these cases it is then easy to write down the desired deformations explicitly.
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PDF链接：
https://arxiv.org/pdf/0710.2641
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