Degrees of generators of ideals defining curves in projective space
作者:
Heath M. Martin,
Juan C. Migliore,
Scott Nollet,
期刊:
Communications in Algebra
(Taylor Available online 1998)
卷期:
Volume 26,
issue 4
页码: 1209-1231
ISSN:0092-7872
年代: 1998
DOI:10.1080/00927879808826194
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
For an arithmetically Cohen–Macaulay subscheme of projective space, there is a well-known bound for the highest degree of a minimal generator for the defining ideal of the subscheme, in terms of the Hilbert function. We prove a natural extension of this bound for arbitrary locally Cohen–Macaulay subschemes. We then specialize to curves inP3, and show that the curves whose defining ideals have generators of maximal degree satisfy an interesting cobomological property. The even liaison classes possessing such curves are characterized, and we show that within an even liaison class, all curves with the property satisfy a strong Lazarsfeld–Rao structure theorem. This allows us to give relatively complete conditions for when a liaison class contains curves whose ideals have maximal degree generators, and where within the liaison class they occur.
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