Paper
Homogeneous Border Bases on Infinite Order Ideals
Authors
Cristina Bertone, Sofia Bovero
Abstract
Border bases are traditionally restricted to 0-dimensional ideals due to the finiteness of the underlying order ideal. In this paper we extend the theory to homogeneous ideals of positive Krull dimension by introducing homogeneous border bases, defined relative to an infinite order ideal. Moreover, we provide two characterizations of these bases: one via border reductors and, most notably, one in terms of formal multiplication matrices. Although the latter condition a priori requires verification in infinitely many degrees, we prove that it is sufficient to check only finitely many of them, thereby obtaining an effective criterion.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.06155v1</id>\n <title>Homogeneous Border Bases on Infinite Order Ideals</title>\n <updated>2026-03-06T11:04:22Z</updated>\n <link href='https://arxiv.org/abs/2603.06155v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.06155v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Border bases are traditionally restricted to 0-dimensional ideals due to the finiteness of the underlying order ideal. In this paper we extend the theory to homogeneous ideals of positive Krull dimension by introducing homogeneous border bases, defined relative to an infinite order ideal. Moreover, we provide two characterizations of these bases: one via border reductors and, most notably, one in terms of formal multiplication matrices. Although the latter condition a priori requires verification in infinitely many degrees, we prove that it is sufficient to check only finitely many of them, thereby obtaining an effective criterion.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.AC'/>\n <published>2026-03-06T11:04:22Z</published>\n <arxiv:comment>23 pages. Comments are welcome</arxiv:comment>\n <arxiv:primary_category term='math.AC'/>\n <author>\n <name>Cristina Bertone</name>\n </author>\n <author>\n <name>Sofia Bovero</name>\n </author>\n </entry>"
}