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Citació: Planas, F.; O'Carroll, L. Ideals of Herzog-Northcott type. "Proceedings of the Edinburgh Mathematical Society", 19 Gener 2011, vol. 54, núm. 01, p. 161-186.
Títol: Ideals of Herzog-Northcott type
Autor: Planas Vilanova, Francesc d'Assís Veure Producció científica UPC; O'Carroll, Liam
Data: 19-gen-2011
Tipus de document: Article
Resum: This paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is the ideals determining monomial curves in three-dimensional space, which were studied by Herzog. In the broader context studied here, these ideals are identified as Northcott ideals in the sense of Vasconcelos, and so their liaison properties are displayed. It is shown that they are set-theoretically complete intersections, revisiting the work of Bresinsky and of Valla. Even when the three elements are taken to be variables in a polynomial ring in three variables over a field, this point of view gives a larger class of ideals than just the defining ideals of monomial curves. We then characterize when the ideals in this larger class are prime, we show that they are usually radical and, using the theory of multiplicities, we give upper bounds on the number of their minimal prime ideals, one of these primes being a uniquely determined prime ideal of definition of a monomial curve. Finally, we provide examples of characteristic-dependent minimal prime and primary structures for these ideals.
ISSN: 0013-0915
URI: http://hdl.handle.net/2117/11327
DOI: 10.1017/S0013091509001321
Versió de l'editor: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7978096&fulltextType=RA&fileId=S0013091509001321
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