边境基地的变形
Deformations of Border Bases
摘要：
在这里，我们研究的问题，推广的主要工具之一Groebner基础理论，即平坦变形的首项理想，边界的基础设置。在表明，直接的方法的基础上变形的程度形式理想的作品只有在额外的假设下，我们介绍边界基础计划和通用的边界基础家庭。在它们的帮助下，这个问题可以被重新表述为在边界基方案上寻找某个有理曲线。用不同的方法构造了边界基格式的消失理想的生成元系，并研究了如何使它最小化的问题，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一个仿射空间.在这些情况下，很容易明确地写下所需的变形。
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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